Why is Bob Saget the future voice for Ted Mosby'?

Yeah this question seems to come up a lot since the Family Guy episode where Peter asked this. Interestingly enough even though it's well known that Bob Saget is the voice of the Narrator he is not credited. No reason has been given so far as to why he is the Narrator. They have even shown Future Ted in the show and he sounds just like Present Ted.

My best guess is that this is a joke that was written and the punchline hasn't been revealed yet, a typical device for this show (such as what happened with the goat). It's supported by this story:

It was earlier speculated that Josh would replace Bob as the show's narrator for the finale, but executive producer Craig Thomas has reassured us that Bob isn't going anywhere for the finale.

Most likely there is a joke involved with the differences in voice.

Bob Saget is a well known name and many recognize his voice, which might be why he's used. It may have also contributed to the show getting green-lit, as there none of the cast was a big name actor at the time. Also, the distinction between future Ted's narration and the current story helps to differentiate between who is speaking at that moment. It would get confusing very quickly if present-day Ted's (Josh Radnor) voice were heard correcting his future-self. For the audience, it would be indistinguishable from the in-scene Ted.

First of all, if you haven't seen the series finale, this answer might be considered a spoiler (it was for me, as I haven't seen the finale yet). But I'm also not going to put the whole answer into a spoiler block, so if you have fear DON'T READ ANY FURTHER.

I found this very interesting article about exactly this question. It argues that How I Met Your Mother is basically a prequel to Full House and Ted Mosby (voiced in part by Bob Saget) is Danny Tanner (played by Bob Saget). Now of course it is clearly not a direct prequel, given the different persons, setting and timeframe, but maybe a prequel in spirit.

As we learn in the series finale, the Mother is already dead for six years when Ted tells his overlong story to his children and this ending was planned this way right when the show started (as also confirmed in the answers to this related question):

Carter Bays has confirmed that the series' tragic close was "the ending they conceived when they conceived the show 10 years ago." Having envisioned a show all about a man who would ultimately lose his wife telling his children how he met her, Bays and Thomas cast Bob Saget in the part - the most famous widower in modern sitcoms.

Furthemore, the article notes some similarities between Ted's group and the characters from Full House:

Ted, as played by Josh Radnor, is Danny Tanner, just with a better sex life and an all-consuming love of architecture. The inherent, series spanning joke about both men is that they are nerdy, 'dad joke' making father figures. They're both the same archetype within their respective series - 'the dad'. Bays and Thomas wrote a part strikingly similar to Danny Tanner, and then cast Bob Saget in half of the part.

Barney Stinson isn't Jesse Katsopolis, yet both are ladies men with a flair for the grand gesture who by their series' end learn the value of family. Marshall Eriksen isn't Joey Gladstone, but they're both pun spewing aspiring stand up comedians who struggle with a work-life balance, yet ultimately believe family is the most important thing.

They're all variations on a theme - oddly specific archetypes that together blend into the same basic friendship dynamic. Add in the alternatingly hard-nosed, professional TV personality (Robin) and loving, slightly lunatic mother and wife (Lily) and you can spot Becky Donaldson too. For some time Danny dates a woman named Vicky Larson. Sadly, their relationship doesn't work out. For Danny, family is the most important thing. For Vicky, her career. As a News Anchor. In New York. Just like Robin. The relationship even begins six years after he was widowed.

Ted's life after becoming a widower could thus be seen as being continued by Full House:

As part of the frantic montage of Ted's key life events in the series finale, we watch him at his dying wife's bedside, and we see him tell his children, six years later, how he met her. What we don't see is Ted heading home for the first time after his wife has died. We don't see him helping his young children to move on with their lives. We don't see, at all, his friends' reaction to the loss.

[...]

The show doesn't show that moment, though, since that moment, where a group of friends come together to help one of them get through the loss of his wife, is where the prequel ends, and the original series takes back over.

Now it is hard to say if it was really that strong a connection to Full House that the creators of How I Met Your Mother intended or if it wasn't just a fitting casting choice to let the father be voiced by another famous sitcom father. But while that article might be a bit speculative (and those kinds of characters can probably be found in many sitcoms in some way or another), it gives quite some insightful arguments and some interesting connections between those two sitcoms apart from a mere voice-actor choice, even if we don't know (or might doubt) if all that was completely intentional.