How far back do I need to watch Doctor Who for it to still make sense?

There are some great answers here already, but as a huge Whovian I wanted to add a little more information.

As a complete beginner to the series definitely start with the 2005 Doctor Who series. The series will make perfect sense and there will be nothing revealed that will leave you confused (or at least nothing that won't be cleared up later in the series!).

There are old enemies/allies from the original series that will appear and you'll not realise it - but that won't affect your viewing experience in the least.

Now, if you watch the Series, like it and decide to consider watching the Original Series, consider the following:

Doctor Who kicked off all the way back in 1963. This is significant for a few reasons. The original series was in black and white. Now, I'm a child of the nineties and as much as I'm ashamed to admit it, a lack of colour really does affect a movie for me. I'm so unused to things being black and white that I find it much deeper to embrace older movies/shows. Of course that's not universal and I've enjoyed some fantastic old films and tv shows - but without question they require far more concentration on my part to really get into. If you're anything like me and you think that a lack of colour (at least for the first few series) would bother you, it's worth bearing this point in mind.

Unlike the original Star Trek, which was in colour and has since been touched up/remastered, the original Doctor Who episodes with William Hartnell do show their age. They're certainly watchable and enjoyable, but you'll need to concentrate and accept some very dark/grainy footage at times.

You'll also need to accept that as times changed, so did the character of the Doctor. Nowadays, we want a fun, energetic, brilliant, slightly sexy Doctor, which is where the likes of David Tennant (10th) and Matt Smith (11th) came from. Back then, the idea of the Doctor was that he would be a very intelligent, slightly dotty man. That's the character William Hartnell plays. An old, clever man, who is slightly mischievous. He by no means always saves the day. In fact, in many situations he's the one who gets them into trouble and his companions (Barbara and Ian, two teachers) are the saviours.

I'm bringing all this up because if you watch the new series, the character that the Doctor portrays is not how it was in the original series (at least to begin with).

Another issue to consider is that in the very beginning Doctor Who had an educational remit. This meant that for every "futuristic" serial it ran, it had to run a serious "historical" serial which would accurately tell a real life historical event (such as Marco Polo, the burning of Rome by Nero etc). Now this remit only last a few series, but it's another thing that's worth bearing in mind.

Finally, if you do decide to go back to the Original Series, there is one more thing you must accept. Due to the wiping policy of the BBC there are a number of episodes of Doctor Who that are missing (mostly Patrick Troughton, the 2nd Doctor's, but also a fair few of Hartnell's (1st Doctor)).

In other words, if you do start watching William Hartnell right from 1963, within a few years you'll start hitting episodes that you'll either have to listen to the audio from (they were broadcast over radio) or you'll have to skip entirely.

Having said all that, the big positive of going back to the Original Series is that you'll get to soak in all the Doctor Who mythology, hear, see, live and breath the universe presented and be a "true" Whovian! But - it is a long (and expensive) haul. Don't expect to finish anytime soon!

Conclusion

Unquestionably start with the Modern Series (2005). If you like it and want more and are considering the Original Series, consider the following questions:

1. Will the black and white/grainy aspect of the stories bother you?
2. Will the low production costs of original episodes bother you?
3. Will the different presentation of the Doctor (not as strong/intelligent etc) as modern Doctor bother you?
4. Will the fact many of the 2nd Doctors serials are missing, meaning you'd have to "skip" them bother you?

If the answer to any of these is yes, then perhaps the Original Series isn't for you.

If the answer to all of these is no, then start watching and enjoying :)

You can start with the 2005 series starring Christopher Eccelston if you want the full Doctor Who experience from when it was bought back to TV

However, if you cannot tolerate the poor special effects or cheesier stories, you could jump forward to the 2010 series with Matt Smith as the Doctor.

The Matt Smith episodes have almost nothing in common story-wise with previous episodes, so this can be seen as a safe starting point as well.

I'm going to disagree with the majority here. I think it is worth watching at least some of the classic series early, in order to get an appreciation for where the show has come from. I'm not going to suggest starting with it, but I think jumping back to it between watching modern episodes could be an enlightening approach (which I wish now I had taken).

I'd also note that it's quite possible to dip in and out of most of the earlier parts of the show without regard to order. It might make sense, then, to watch the episodes in the order where the ideas they contain become relevant.

My suggestion as to viewing order, therefore, is something like this:

• Watch Rose, the first episode of the 2005 series. This will give you a taste of what the modern series is like.
• Watch Spearhead from Space, the first episode of the third Doctor's tenure. This will make an interesting comparison, because the enemy it deals with is the same enemy that turned up in Rose.
• Continue watching the 2005 series up to (but not including) Dalek. Before watching that, it's time for a history lesson.
• Watch original series stories: The Daleks, Dalek Invasion of Earth and Genesis of the Daleks.
• Watch the remainder of the 2005 series 1.

By now you should be hooked. You have an appreciation of both the modern and the original series. Go back and fill in some of the gaps. Try interleaving modern and old stories (although be aware that the ends of a lot of the classic stories feed directly into the next story in sequence, particularly starting with Baker's episodes, but they did do this sometimes before). Don't try to watch everything: many of the older episodes aren't worth watching, particularly the black and white ones: a lot of Hartnell's episodes are slow paced and frankly boring. Most of Troughton's are missing (but do watch at least the highest few rated of the ones that are available: Tomb of the Cybermen and Invasion are both brilliant, and War Games is really good if you're up for a long story... it took me 5 days to watch, but was well worth it). After that things start improving, but for me the show really picks up around the time Baker took over, and maybe that's where it's worth watching it all from. The companion(s) have a lot of influence over the tone, and IMO Sarah Jane Smith was one of the best. She was companion for Pertwee's last series and the first series-and-a-half of Baker. Make sure you've watched at least some of these before you get to School Reunion (from the modern series 2).

When you're skipping around between the classic episodes, you'll want a good guide to the episodes with details about ratings, which recurring enemies are involved, and so on. I use this one. It's not as detailed as others, but it includes the rankings of each episode in a poll conducted by Doctor Who Magazine a few years ago, which makes it very useful.

Edit

Some more thoughts on specific things to watch and when:

• One of the other answers includes a list by Neil Gaiman, which made me think about the episode he wrote in the most recent series, Nightmare in Silver. This is a Cybermen story, and for the most part the Cybermen in the modern series are not really connected to the original series Cybermen -- unlike most of the other enemies, they completely rebooted the Cybermen, gave them a new origin story, and so on. So while for the rest of the enemies (particularly the Daleks and the Master) I'd suggest going and watching some of the classic stories about them before seeing the new ones, I don't think this really applies so much to the Cybermen. Except: Gaiman's story is actually about the classic series Cybermen, not the modern ones -- it is more like the original stories stylistically, and includes reference to a couple of plot points from the original series that haven't previously been incorporated into the modern series (i.e. the future war between humans and cybermen that is in the history of most of the original series episodes featuring them, and a weakness they have that was exploited a few times in the original series but not mentioned previously in the modern episodes). So, while there's no need to catch up on the cybermen before then, at least prior to watching Nightmare in Silver catch up on the relevant classic episodes: Tomb of the Cybermen, Invasion, Revenge of the Cybermen and Earthshock.
• Revenge of the Cybermen is the last part of a continuous sequence of 4th Doctor stories which begins with The Ark in Space and also includes Genesis of the Daleks. While it isn't critical to watch these in order, I recommend doing so, as they're all good stories.
• Earthshock, also mentioned above, is a particularly significant story. You'll want to have seen some of the stories from the season before it and earlier in the same season before watching it. The E-space trilogy (which consists of Full Circle, State of Decay and Warrior's Gate) is a reasonable place to start, and the next three episodes that follow it (The Keeper of Traken, Logopolis and Castrovalva) which also form a sequence of stories by themselves are worth watching at this point too. Kinda is divisive. Some people like it, others hate it. Read reviews to see if you think it'll be worth watching.
• The Master first turns up in the third doctor era, and has a few great stories there (Terror of the Autons and The Daemons are particularly good), but his best stories are in the 4th and 5th Doctors' eras. The Deadly Assassin is one of the best stories in the show (and one of only a handful that don't feature a companion). The Five Doctors is a classic in its own right. I'll avoid mentioning others, because the show's producers often tried to keep it a surprise that the Master would be in a story, even to the length of using aliases for the actors who played him rather than putting their names directly in the credits. You can look them up if you feel you're missing anything, but I'll note I've recommended most of them here anyway.

If you're just starting out, then starting with the reboot makes sense. They tried to make a fairly clean start and work back into the 'legacy' villians such as the Daleks and the Master.

If you want to backfill from there, there's two DVD sets of the "Doctor Revisited" episodes, where they do a show-and-tell about the prior Doctors leading into one of their episodes: for Hartnell it's "The Aztecs", for Pertwee "Spearhead from Space" (his intro), Tom Baker "Pyramids of Mars", etc. That should give you a good taste for the style of the prior characters without drowning you in twenty-five years of material.

Start with Doctor Who (2005). It's good to understand and works like a reboot (little going back sometimes). It's also a fresh start of the TV series after a long time and also had good success.

Even said the same over scifi.stackexchange.com.

While I totaly agree that starting at the beginning of the 2005 reboot is the way to go, I'm going to make an alternative suggestion for if you want to go back a bit further. Start with Jon Pertwee (Third Doctor) either at the start of his tenure, or at the point where the series become colour. You will miss much less ny skipping the first two doctors than the third and fourth. Why?

• The show became much more science-fictiony and much less historical around here
• The budget went up significantly, as did production values
• This is where the Doctor stopped being a grumpy old man and began saving the planet (and later the universe) on a frequent basis
• Virtually all the enemies that show up in the reboot make frequent appearances in this period, and you won't lose much of their history by skipping the first two doctors.
• You'll meet Brigadier Lethbridge-Stweart and UNIT, which will add some enjoyment to the reboot
• Virtually all the episodes are easily available after this point

Okay I'm with the bulk of the above opinion, starting with the reboot is far and away the best option.

If you want a taster of the original stuff without committing to hundreds of hours of tv there where 2 Peter Cushing movies they aren't cannon but give an okay jumping on point and are in colour with slightly (very slightly) higher production values.

Also the companion show to the 50th anniversary special and Adventure in Time and Space gives a nice grounding to the old series.

But it's worth remembering for almost 5 decades people have been jumping into it on whatever episode happened to be on and figuring out from there and there's a new Doctor due imminently which is usually a good starting point (The old stuffs not going anywhere go back and catch up when you think you need it/you'll enjoy it there's no shortage of people to give you the reference points online)

As far as I've seen there are not a whole lot of overarching plotlines in Dr. Who other than "The Doctor is a Time Lord" and "Daleks are bad", and for the most part each episode is a self-contained story with little to do with any other. In the cases that there are callbacks to other stories it's usually concisely explained with something like "don't blink, if you blink you die" or pretty apparent like "Cybermen are also bad".

And like someone else said in here, if you're not confused then you're probably not watching Dr. Who.

Now moisturize me.

I like a lot of the suggestions, but I wanted to report a suggestion from Neil Gaiman (who wrote several episodes of Doctor Who in addition to several bestselling novels), which I think is quite good:

I’d watch some Doctor Who, if I were you.

Here, I’ll make you a watching list. Netflix is your friend:

Watch an episode called BLINK.

Watch The Girl in the Fireplace.

Watch Dalek. (Yes, the Doctor looks different. Same man, though.)

Watch The Empty Child two parter.

Watch The Doctor’s Wife (I wrote that one, which is why I’m putting it on the list.)

Watch City of Death (it’s a classic series of shorter episodes from 1978ish, written by Douglas Adams).

Somewhere around there, start watching the New Series 1 with Rose and just come forward normally.

The New Series 1 he is referring to is the same 2005 Modern series that many others have mentioned; its first episode is entitled "Rose."