Capcom is a legit contender for greatest development studio/publisher of all time in my mind. Things have really been rough the past few years with them, but they're still putting out some great games and don't look to be going the way of Konami just yet.
I'm applying the same "1 game per franchise" rule that many other people have, and am going to try to keep some genre diversity as well. As such, mine might be more of a "10 essential Capcom games" list than a pure top 10.
Resident Evil 4 - One of the best action/TPS games ever made. Those genres were pretty much all anyone focused on making last gen, and they still couldn't top it.
Mega Man 9 - The pinnacle of the classic series. Perfect in nearly every way.
Street fighter III Third Strike - Insanely fun, deep, beautiful, and easy to pick up game. The only other 2D fighter that comes close is Darkstalkers 3.
Rival Schools - It took Capcom a while to get 3D fighting games right, but they hit it way out of the park with this one. No idea how it holds up from a competitive standpoint, but it's every bit as fun to pop in now as it was in middle school.
Breath of Fire IV - Leave it to Capcom to make an astoundingly gorgeous, un-apologetically oldschool JRPG in the waning years of the PS1, when everything was angsty FMV and 3D or bust.
Tatsunoko vs Capcom - The most fun Capcom vs. game to me (other than Match of the Millenium), with the best cast.
Monster Hunter 4 Ultimate - One of the biggest and most rewarding games I've ever laid hands on.
Mega Man Zero 3 - Any game from this astounding series could make the list, but I found three to be the most enjoyable.
Powerstone 2 - I'll be honest, I can't even say for sure that this game is good. What I can say for certain, though, is that it provided every bit as much fun as other legendary local multi games like Smash Bros. and bomberman. Me and my friends played this and the first for hundreds of hours without getting bored.
Okami - A flawed but beautiful and endlessly engaging, sprawling ode to The Legend of Zelda and Japanese culture. How could I not love it?
I still really need to get around to the DMCs, VJs and Godhand.