I do have plenty of experience with this.
I ran a 3-years campaign which was basically modern-day Call of Cthulhu, set in my own country (Italy). Actually we used mostly the rules and the world was more like Dresden Files (even if 25 years before Dresden's novels) than Lovecraft.
This was quite popular and inspired some spin-offs among fellow players, so I was exposed to the idea both as a referee and as a player.
We were all in our early-20s so I ruled that while keeping events in the current year, everyone should create a 10-year older version of themselves (most of us were in UNI and I wanted PCs that could actually do things, both in terms of skills and in general independence).
(Retrospectively this also allowed players to "deviate" a bit from their own self, in the sense that they could at least choose a career path).
Stats were rolled but I (as GM) had the right to mandate a reroll for things that didn't make sense knowing the real person. This was done only for things like people rolling pathetic INT stat, or body size too out of whack with their real body etc.
(I am not perfectly sure of this anymore, but I think I made them roll 2d6+6 instead of 3d6, removing the risk of excessively low stats... I toyed with the idea of having people vote on each other's stats and average, but in the end I decide this wouldn't be practical so I ditched the idea from the start).
Profession was selected more or less freely. In some cases people opted for "unrealistic" stuff (one of the players became a private investigator) but I allowed it to have a more interesting mix (in Italy private possession of firearms is strictly regulated, so this was also the only one who had rights to bear a weapon).
Nobody else was allowed to get absurd things like "mercenary" or "fighter pilot", though.
Interestingly enough, most players were happy to play themselves, but some decided to roll a completely unrelated character instead (a DBA opted for being a support guitarist for pop-rock bands - i.e. the kind of guy who gets in the in-studio credits).
Thos who opted for not playing themselves just told they didn't like the idea, and I didn't press the point because for me it was the same (I just wanted "normal" people in the campaign). For those cases we just invented a retro-connected story to make them mingle with the ones that had opted to play "themselves".
For a bit the idea worked: having to deal with "real world" consequences, players tried to remain on the right side of the law, and worked hard at making good use of what (and whom) they knew in real life. Whenever they introduced NPCs ("I have a cousin who is a doctor, he will be glad to cure my wounds without calling the police") I vetted them to be sure they weren't just inventing stuff.
In retrospect, being able to use real-world knowledge and real-world contacts/friends/relatives helped the PCs to be more effective at the start of the campaign (later they acquired plenty of uncanny, powerful friends and enemies, as the weirdness level ramped up).
N.B.: My reason to structure the campaign around "real world people" came from me growing disgusted by how players (mostly veterans of old-days AD&D) tackled any kind of issue in-game: i.e. "kill it, loot the corpse... can't kill it? kill something else until we get enough experience to get back and kill it".
I wanted a change in paradigm, and I hoped that playing "yourself" would help players getting out of the stereotypical AD&D party mindset.
In that sense, it worked. For a bit. I wasn't interested in making this a psychological study, so I never sacrificed "fun" for "realism": a bit later things started getting surreal - but this was due to the direction I wanted to give to the campaign, not a problem with the PC identities.
So, my advice:
- do not force anyone to play themselves if they don't like the idea. Make them generate characters in the normal way for your system.
- personally I think the idea has some merit if you want to play in some variation of real world. Having a group of D&D players magically transported in a fantasy world may be fun but I don't think it adds much in terms of value (YMMV, of course).
- if you want a "gritty", realistic campaign you have also to take in account that some of the players will know more about their own job than you can possibly do. This may create problems if they start poking holes in some of your ideas. But the real problem is that you may have little ability to double-check or overrule what they say about what their PCs can do.
(Case in point: my PCs routinely took strange artifacts to a real world guy with a degree in Physics to have them analyzed... he even guest-starred - for real - in a session where they were dealing with a painting showing some bizzarre properties... the guy bombarded me with questions about what the results of his various tests were, and I had really a hard time keeping pace).
- death of a character is a problem. Not just because it may be uncomfortable for the player (my own PC was killed after a few sessions in a "real-world campaign" with another GM, so I know what I am talking about) but also because replacing "real me" with a rolled-up character creates continuity problems: the other PCs have much stronger bonds than what you could expect in a "normal" party.
- In general terms (unless you play only with US Army members or Police officers and so on) "real people" are fairly ineffective in terms of average RPGs. Especially regarding combat. This creates two problems: first of all you have to constantly doublecheck conflicts to be sure that your PCs stand a chance. Besides this, you have to be very careful during character generation to find a way to express their actual competences in game terms.
Case in point: I am currently a 3rd Dan in Aikido... what will this mean in your game system of choice? If it is something like GURPS, it has some equivalence in terms of "number of hours practicing a given skill->X points in that skill" and this is probably the best way to do that. But most other systems may be lacking this kind of rules and you will have to eyeball things a lot.
Someone else mentioned the fact that interpersonal relationships (like having your wife or parents as NPCs) may be difficult to handle. I agree with that, too - and I have to admit I steered clear of that as much as possible. We were young, and most of us were the stereotypical nerds, with no GF etc. The "make yourself 10 years older" glossed over that part, so all of them played "singles", no kids etc.
If I had to do this today I would surely try to handle this in a more appropriate way, but for sure you have to think about how far you want to go (as a GM) in involving NPCs who are actually "real people".