My default approach is always: watch the movies in the order that they are released. My reasons are:

1. I want to experience the "historical" perspectives of the people who watch the films as they come out. An easy example of this is the Star Wars series. I haven't seen any of them yet (gasp!) but when I get around to do it, I will watch 4,5,6,1,2,3. This way, I'll get to see the supposed old-school magic first and then the new-school prequels that seem to disappoint many fans. In sum, I want to see things in the same order that those fans have seen.
2. While film makers usually make new releases in a franchise in such a way that new viewers who have no prior exposure to the franchise can get in, these film makers must have in mind the people who have seen the previous installments in the franchise. Thus, I believe that you can get more out of the new releases if you have seen things in order, regardless of whether the new ones are prequels or sequels.

Avoiding spoilers

If you watch Underworld 3 before Underworld 1, you will know more about the backstory than Selene does, so you’ll be waiting for her to catch up with you. If you watch Underworld 1 before Underworld 3, you’ll mostly know how Underworld 3 ends before starting it. You’ll get spoilers either way, but the spoilers are probably somewhat milder if you watch Underworld 1 first.

Selene’s story

Underworld 1, 2, 4, and 5 tell the story of Selene. Underworld 3 gives backstory that doesn’t have much to do with Selene, and it contains information that Selene doesn’t necessarily even know. If you’re primarily interested in following Selene as she discovers the history of the vampires and lycans, then this is my recommendation:

• Watch Underworld first.
• Watch Underworld: Evolution, Underworld: Awakening, and Underworld: Blood Wars in that order.
• Watch Underworld: Rise of the Lycans anytime after the first film, or skip it entirely. The usual placement would be in release order, between Underworld 2 and 4.
• Watch the Underworld: Endless War stories at some point, if you’re going to. Release order puts them between Underworld 3 and 4.

Chronological order

You’re right that the main events of Underworld 3 occur before the main events in the other films, but complete timeline is more complicated than that. If you want to follow the story in chronological order, do this:

1. Watch the first 8 minutes of Underworld: Evolution. Stop when it says, “Screen Gems and Lakeshore Entertainment.” This portion is dated to the year 1202.
2. Watch Underworld: Rise of the Lycans. Selene’s narration in the first minute of the film is misleading: the film starts in the early 13th century, and the main portion of the film is set in the early 15th century. Stop or mute the film quickly at the end (time 1:22:33 on the DVD), when the screen fades to black and you start to hear, “but let me tell you a little something...” The video won’t contain any spoilers, but the audio will. You can unmute the audio when the credits start.
3. Watch Underworld: Endless War, parts 1 and 2, which are set in 1890 and 1967.
4. Watch Underworld, set in or near 2003.
5. Watch the rest of Evolution. The flashback 55 minutes in predates the main events of Rise of the Lycans by a couple decades, but it’s too short to separate it from the film and watch it in chronological order.
6. Watch Endless War, part 3, set in 2012.
7. Watch Underworld: Awakening.
8. Watch Underworld: Blood Wars.

As a fan of the Underworld series, the (my) recommended viewing is:

1. Underworld (The Extended Director's Cut preferably): This starts the series, and if not seen first, would be majorly spoiled by the other movies. Much of the allure of this film comes from the mystery revolving the Lycan/Vampire blood feud, and the characters in it. If you remove the mystery (from watching Rise first), everything feels like false tension. If the audience knows everything Selena doesn't, her character seems moronic.
2. Rise of the Lycans: Fills in most of the new information for the series. It also pairs nicely with the Selena/Michael & Lucian/Sonja star crossed lovers theme.
3. Evolution: Pretty much a self contained story Re: William and Marcus. The Selena/Michael plot is weakened, and seeing this after Rise prevents the love story from seeming cheapened. This movie is pretty much just a standalone action film compared to the world building down in Underworld and Rise.
4. Awakening: The post-time skip sequel to Evolution. Selena is chasing after the lost Michael, and dealing with the kid she was knocked up with in Evolution. NOT A PREQUEL.
5. Next Generation: Another time skip sequel to Awakening. (October 2016)

Optionally, there is also Underworld: Endless War, a anime short that follows Death Dealer Selena dealing death to a set of Lycan brothers. It has three parts, one set before the events of Underworld in Victorian paris, another set in the late 60s again pre-Underworld, and a third set after Evolution/before Awakening.

Finally, there is a 6th movie in planning, and a TV show that's a spin-off/mostly unconnected to the plot of the movies. A shared universe. According to producers Len Wiseman and Mark Goffman

I suggest watching it in order as the movies were intended. Because the rational that occurs in the first one has a shock moment that is ruined if watched out of intended order. However if you strive to still watch chronically then it would actually go 3,1,2,4. The forth is not a prequel like someone else previously stated.

watch them in the order they were made because in underworld(1) you have a surprise part that would be ruined if watching rise of the lycans(3) first. i watched it in release order and it seems to be the best for me. the prequel just gives further understanding into how it all started in more depth but could ruin the first two movies if watched first.

Watch them in order or else there are spoilers in the later ones even though they are prequels

The order:

1. Underworld: Rise of the Lycans is first because it has characters in it that are in Underworld. The end of Rise of the Lycans is an intro to Underworld.
2. Underworld is second because it carries on from Rise of the Lycans.
3. Underworld: Evolution is third because it includes the characters from Underworld and it continues the story from Underworld.
4. Underworld: Awakening is fourth because if you watch the third one (Evolution) it continues off of that specific movie.

You HAVE to watch them in certain order otherwise if you have never seen them before, you will be confused on the whole back story and how it all began and who the characters are. I've watched all 4 at least 10 times each and after watching them for the first time, it is not hard to put the puzzle pieces together after watching them all. The order again is: Rise of the Lycans, Underworld, Evolution, and Awakening. You're welcome:)