Have you ever played a game that was generally considered as really bad and you had a blast playing it?
I remember when I bought the latest Alone in the Dark (X360 version) it got mostly terrible reviews - IGN gave it a 3-ish if I remember correctly. I also remember that the worse the review I read the more compelled I felt to play the game :) I had so much fun with AitD even though it's flawed in many areas. I have finished it 3 times and I'll probably return to it again. :)

It depends. Under A Killing Moon got bad reviews in the British press so I only knew about it getting panned (didn't have access to American reviews where it got glowing reviews) so I thought people didn't like it yet I loved it. Of course, a few years later I discovered it's considered a classic by many and PC Gamer (among others) were just being anal about the game.
But it's mostly games where the atmosphere really grips me. Gabriel Knight 3 got relatively poor scores around here as well for example but I loved the atmosphere.

Maybe because they loved the original so much that no matter what the new one did it wasn't good enough.

Now, i don't really remember what reviews Sid Meyer's Covert Action had, but i remember mr. Meyer wasn't happy with it at all, yet i still play that game today, and love it.
Then, Settlers 6: Rise of an Empire, which has 66/100 on the Evil MetaCritic. And that game had some of the worst scripting i have ever seen [yes, worse than EA's take on C&C]. I'd have to add
And then there's The Detective Game for the C64, which generally got some bad reviews, ZZap somehow gave it a 78%, which is still too low.
There were a lot of other bad games i've played when i was a kid, mostly because of the "i wonder what this is about" childish exploration need, yet i don't remember the titles.
I'm more concerned about bad games getting good reviews. Like [now someone is going to kill me] Settlers 2, which looked lovely, but played like a steamroller on ice while drunk, and had a pretty weak campaign [the Roman one, not World which was added in Gold].
I bet there were more games but i just can't remember, i'll get back to You when i remember something more. ;)

A game that received bad reviews can be a good thing, indeed, cause when you play it you don't expect much of it, and so you can be surprised.
In the case of the lastest Alone in the Dark, I haven't played it, but it's the typical exemple of a game that has been talked about so long before its release (as often, the fault, in first place, is from the publishers who claim that their game is revolutionary) that many gamers expect very much of the game, and you can only be disappointed. That, and the fact that it's a sequel of a long-time famous licence in this case.
What I can't stand is that the mix of "high expectations" and "disapointement" often leads to very very bad reviews, claiming that the game is "the worst game ever" or that kind of crap.
Disapointing doesn't necesserally means bad game. There are loads of unknown and quickly developped bad games.

Heroes of M&M 4 - I like it despite all the QQ, curses, uproar against it and whatever else. Yes, quite a lot of people I know like it, but it has far more haters who hate everything on it just because it isn't HoM&M3....

If you want QQ just look at Command & Conquer 3 and Red Alert 3. Both games I thoroughly enjoyed.
Aliens Vs Predator (the recent one) was slated by most of the media but again I really liked it.
Rogue Trooper was ignored by the media because of a little game called Gears of War, yet I enjoyed the former more.
Famously Deep Fear on the Sega Saturn was awarded a 5/10 by EDGE magazine despite being superior to Resident Evil in many respects. For one thing you could move and fire :O

I really, really want to get my hands on AvP... I loved the two PC-only games. You just can't go wrong with a franchise like that :D... unless you are making a movie.

Jedi Power Battles on PS1.
The game, especially at this time - around the release of Episode I movie and all the games based on it - has received bad or mixed reviews.
It was not that great in solo mode, but, hell, it was so fun in co-op mode. I remember hours and hours with my bro on it, trying to get highest score at each level to gain all combos and bonus points.
We've replayed it last year, still with a lot of fun.

Mega Race 1 and 2. A couple of very fun, if imensely ridiculous games.
Robot City is one of my all time favorites and I don't remember it being fairly well reviewed.

QfT.
BTW - I hated HOMAM3 for what it did with my awesome HOMAM 2(fucked up units, totally awful render graphics...)

I agree about alone in the dark, and another IMO underrated game, althou not necessarily bad, it was getting about 6/10 from reviews: Raise of the Argonauts. I love that game. It's just ... Fantastic.
Bah, graphics are precisely what I hated about Heroes 4: The game was just ... So ... Ugly. At any rate, there was a plenty of things it did right, but almost as much it did wrong. Shame really, it could have been an awesome game.

Yes ugly, but not that ugly like in HOMAM3. They should make wake of gods for HOMAM IV, to repair it, make it better, not try to get HOMAM 3 on HOMAM4 style.

Wake of Gods for HoMM4? FFFFFFUUUUU
Equilibris is more than enough.