OK, I'll ask then: Is it a James Bond game? Could you please describe the setting?

I played a few that were asked here and would've guessed them immediately had I seen them first: Planescape Torment, both Icewind Dales, Neverwinter Nights. Some I guessed because I played them (Commandos)., while some because I did a bit of search on wikipedia or moby games. A few I did play but didn't guess from the description until someone gave the answer.
It does seem though that a lot of the games described I haven't played, and some even haven't heard of. I don't play a lot of adventure games.

Personally, I haven't played many of the games (including The Witcher 1, shame on me). Most of the time I don't have the slightest clue of what the game might be.

Nope, it's not a James Bond game! :)

It's set in Manhattan, New York, but you also get to visit other places including a secret hideout of the villain, who can sing!

"Well boys, we have another mission to do!"
You could always try the classic "Can you describe the characters?" question. ;)

As to your side question, I haven't played most the games here, I've only heard about them or read up on about them (incl. having seen trailers or screenshots etc.), so with the exception of a handful of games like some of Black Isle RPGs I'm also in the "haven't played most of the stuff" camp. However that's what makes it fun for me (besides recognizing those I've played, but so far those were either guessed before I saw them (eg. Planescape :)) or I didn't get that far in the game to recognize the level); because I've heard about a lot of games it's actually quite fun to puzzle the pieces together. :) I don't usually do research though, just search around to confirm what I think or find out more info about the game I'm thinking might fit.

So since no one took the bait: Can you describe the characters?

Sure thing! They are four brothers, all in black and white, and to top it all, they have freakin' flippers! One of them is the clever and resourceful leader, with great presence and good team planning (who essentially pulls the whole group together and without him they wouldn't be such a good team), another is a genius who invents various gadgets and is your typical quirky, sometimes mad scientist who also does world threatening experiments (confident that they will not destroy the world) and comes up with solutions to various problems, then you have the idealistic, very optimistic but at times a lot naive rookie who believes in high moral values, love and pink unicorns, while the last one is your demolitions man - he loves bombs and anything that creates explosions, he is very brash, impulsive and can get very excited about his hobbies (or angry about stuff in a rage that quickly passes and doesn't hurt anyone, it's actually very funny), and he can produce at a moment's notice almost any item or weapon they currently need for the mission at hand or any other event.

No, and they're not. :)

Penguins of Madagascar? :)

It really sounds exactly like that :D

Yep, you're right! Wednesday saw the release of the new Penguins of Madagascar movie, so that's why I thought it'd be a very appropriate game to choose (although I bet this movie will have another game as well, as the one I was thinking of was released back in 2011).

Also, whether you are a fan of the penguins or not, watch this short Penguins of Madagascar video, you'll love it!

You'll miss out on lederhosen if you don't. ;)

All right, my turn then :)
What in the fuck's name is this place? My life've been rough, I might tell you. As a biker I don't fuck around and both my revolver and my shotgun are always ready for action. But now I'm speechless - materialized in this strange place that looks like quickly built (and quickly left to rot) industrial park and attacked by countless monsters. Zombies, mostly, but also mutants and some fuck-weird mythical creatures from time to time.
Something's fucked up with time and space here. First, a minute lasts 61 seconds. Second, after (roughly) 15 minutes pass, I'm teleported to some other place. I've seen 3 of those. And I've seen some soldierboy and i think a cop from the distance. Seemed as confused as I am. Does it ever end? Is there a way to escape from here?

Blood 2?

Nope :)
First hint: quickly built and quickly left to rot = shitty level design :)

Is it a shooter game?

Yes it is.
First person shooter, I might add.