So... I spent much of last night finishing off Heavy Rain, and very much enjoyed it. I've had my PS3 for a few months now, but it's taken a while for us to get properly acquainted. I think it's time we spent some serious 'quality time' together.

Anyone got some game recommendations for me? I've got Enslaved and Bayonetta waiting, but I'm sure there are many more essential additions to my library...

Bear in mind I'm pretty useless at anything FPS, 'though if it has an easy mode I can generally manage... and war games make me fall asleep and/or cry. Medal of Honor came packaged with the PS3, and I don't think I'll ever even bother opening the shrinkwrap.

Storylines, characters, setting, atmosphere and quirkiness are far more important to me than gameplay.

So... I spent much of last night finishing off Heavy Rain, and very much enjoyed it. I've had my PS3 for a few months now, but it's taken a while for us to get properly acquainted. I think it's time we spent some serious 'quality time' together.
 
Anyone got some game recommendations for me? I've got Enslaved and Bayonetta waiting, but I'm sure there are many more essential additions to my library...
 
Bear in mind I'm pretty useless at anything FPS, 'though if it has an easy mode I can generally manage... and war games make me fall asleep and/or cry. Medal of Honor came packaged with the PS3, and I don't think I'll ever even bother opening the shrinkwrap. 
 
Storylines, characters, setting, atmosphere and quirkiness are far more important to me than gameplay.

God of War 3 is pretty epic, if you don't mind quite a short game. Uncharted 1 and 2 are both great.

The obvious: Uncharted 1 and 2.
Also if you're into "atmosphere" you really gotta give Demon's Souls a try.
 
I also highly recommend PSN's PixelJunk Shooter (the first one, I haven't played the second) and there's a demo for you to try for free :)

InFamous and Uncharted also if you like RPGs give Oblivion or Dragon Age 1 a try

You might try Valkyria Chronicles, it's an interesting Action RTS.  Super Stardust HD and as someone else recommended, Pixel Junk Shooter is fun (so is Monsters) and you can demo those.  I'd go with Little Big Planet 2 if you haven't tried out that series.    If you haven't played Mass Effect 2, that's a bargain on the PS3 since you get all the DLC for free.  Batman Arkham Asylum is really good.  The Ratchet and Clank series is always a great distraction as well.  Also, just browse thru the PSN store for demos and see what you can download on demo to give it all a try.

dead space 1 and 2,  
mass effect 2,  
sports champions (if you got a move bundle)  
need for speed hot pursuit 
assasins creed 2 and brotherhood 
burnout paradise 
split/second 
red dead redemption 
god of war 3 
skate 2 or 3 
flower (psn) 
infamous 
uncharted 1 and 2 
batman arkham asylum  
rock band 3 
dj hero 2 
metal gear 4
trine (psn) 
thats some of em'

woohoo, thankyou lovely people! 
 
mass effect 2 i have played and loved on the pc, but i'm tempted to buy it for the ps3 anyway to have a second playthrough and make my boyfriend play it. same with oblivion and dragon age, played and loved on the pc :) i already have a pc and 360, so i'm particularly interested in ps3-only games, or games which are significantly better on that platform!
 
so far i'm definitely most tempted by uncharted 1 and 2, had a look at some trailers and it looks great.
 
games with names like 'killzone' and 'god of war' are so offputting for me, they clearly market these games at fourteen year old boys and don't stop to think about the wider audience. didn't try mass effect 'till it had been around for ages, for example, because all i saw when i looked at it was an ACTION NAME and a BIG MAN WITH A GUN on the cover. i had no idea how much personality the game actually had.
 
anyway, i'm gonna go through your suggestions and check out some videos and reviews, THANKYOU AGAIN! :)

For atmosphere you should check out Demons souls, its one hell of a game, with abit of difficulty, if you can see past that 
 
Uncharted 1 and 2 are very enjoyable games, a mix of third person shooting, platforming and very slick voice acting

@kittencake:

Hey dont forget to Try out Crysis 2 and the Resistance seirse (3rd game coming out september 6th).

" God of War 3 is pretty epic, if you don't mind quite a short game. Uncharted 1 and 2 are both great. "

If you haven't opened bayonetta I'd say take it back. Sega did a poor job porting it. Check out Vanquish instead, it's also by Platinum Games.