Like others have said, you should check out game videos and demos to find out what's right for you.
RPG - this is the genre you asked most about so here's my recommendations:
1. Valkyria Chronicles - definitely #1, couldn't recommend it more. Story seems generic at first but continually surprised me, the battles get consistently more epic and strategy-welcoming as the game goes on, the art style is beautiful and the music is from the FFXII/Ivalice games composer. Great stuff all around. Should be cheap now.
2. Demon's Souls - Unless you've been playing "current gen" games intensely over the last few years you probably won't have a problem with the difficulty. It's very trial-and-error, but you always learn. It's got incredible atmosphere and just makes you want to keep playing, to make it to that boss, learn how to beat him, get great loot and souls then move on.
3. Disgaea 3 - haven't played it, but the consensus seems to be that it's a content-packed game that is right up any SRPG fan's alley. I hope to get it soon. Should be cheap now.
FPS - the dominant genre of this "generation", here's my recommendations for PS3 owners.
1. Killzone 2 - bluntly, this is the game that shows off what the PS3 can do. Every time I go back to it I'm increasingly amazed at how much effort was put into the graphics, enemy AI, art design, detail, movement, shooting, pretty much everything. Just get ready for the movement because it's so finely tuned into a heavy feel that it's a new experience for most FPS players.
2. Resistance 2 - I know Vivi22 has a different opinion, but to each his own. Most reviewers concluded that this game improved on every aspect of the original. The single player was incredibly epic to me, and is one of those few moments where a FPS can get boss battles done right. 60 player competitive, 8 player co-op with maps and balancing crafted to support smaller, intimate games as well. A lot of us on EoFF have it and I'd be willing to play anytime.
Action/Adventure
1. inFAMOUS - Play the demo, because videos can't do justice how smooth and fun this game is to play. Tons of missions plus a second playthrough guaranteed since you want to go to the extremes with the karma system.
2. Uncharted Series - there's really not much to be said at how great this is. While most games nowadays focus on one aspect - shooting, racing, etc, it's fun to get into one with platforming, puzzle solving and competent shooting and melee, not to mention a great story with amazing acting. The first one is a really great game, but the second is just phenomenal, as evidenced by all of its Game of the Year awards. I would recommend playing the original first if you can find it for cheap.
3. Heavenly Sword - This was the first game that showed what the PS3 was capable of and defined the "Blu Ray Experience" in gaming. Amazing graphics, smooth gameplay, incredible animation and voice talent, they put a lot into it. It's short, though, so look for a good price.
Racing - I wasn't the biggest racing fan before this generation so I can swear by the quality of these
1. Motorstorm Series - these are incredibly fun games with great online and a little bit of strategy thrown in there to round it out. Motorstorm is just a great time. The sequel (Pacific Rift) is considered better, but it lost some of the course mechanics of the first and might not be as free flowing. Still, it has 4 player split screen and is indeed plausibly better.
2. Wipeout HD - don't let its "downloadable title" status fool you, this is a full retail game, the modern iteration of a great series. A bunch of us have it here on EoFF and with the Fury expansion there's plenty of content to get your hands on.
3. Gran Turismo 5 - you might want to skip Prologue and wait until the full game comes out this year, there's a time trial demo out now for you to get a hang of the new physics engine. The demo is apparently an old build because everything I've heard from people who've played it at trade shows, is that it simply cannot be overstated that the graphics are JAW DROPPING, and the game promises to be the most complete Gran Turismo yet.
Downloadable Games - Wipeout HD is a given here, but here are some of the more, well, conventional downloadable games.
1. PixelJunk Monsters - it's familiar with its Tower Defense mechanics, but don't be fooled, this game invites a lot of strategy and you'll desperately need it to get past a lot of the stages. It's got a great art style and pleasant music, totally worth the money and a good amount of play time for your buck.
2. PixelJunk Shooter - the latest game in the series, this is one of those old school, rotating, aircraft shooter games where you explore various locations in 2D. Just like the other PixelJunk games, it's got great visuals and music. This is a game you'll play on a rainy day for hours on end.
3. Fat Princesss - a great multiplayer game with various game modes, a unique presentation to it and comical tone. There's surprisingly a lot of strategy and team work required, so this one will have plenty of play time for you as well.
The Big One
Metal Gear Solid 4 - simply put, this is a gigantic, glaring reason to own a PS3. I completely stand behind the statement that this game is miles upon miles ahead of anything else released this generation. In terms of gameplay, story, acting, music, sound, there's just no contest on the PS3 or XBox 360. Killzone 2 and Uncharted 2 may have outdone it on the graphical level, but the visuals are still undeniably better than anything on other consoles. One of my favorite games of all time and living proof that this generation doesn't have to be watered down.
So that's my list, all of these are PS3-exclusives by the way. The only one I haven't mentioned is Little Big Planet. All I'll say is that, more than a year after its release, you can still easily and immediately find amazing, unique content created by other users on the PSN. There's plenty of great multiplatform games out there for you to check out as well.
BTW, my PSN ID is rmx687.