I already have a few games on my list (Metal Gear Solid 4 is absolute #1 on that list, I refuse to buy any PS3 games before I buy that), but I would like to know what some of your reccomended games are. 
 Games I've got in mind: 

• Motorstorm (1 and 2)
• Resistance (1 and 2)
• Uncharted (1 and 2)

Infamous,  It's a super awesome open world game. Like crackdown. Also it has at least two good play throughs  in it.
Killzone 2 , 
Little Big Planet (if you like creating and trying out community stuff)

Everything!

Ninja Gaiden Sigma if you want to smash your controller. that game is HARD. 
Street Fighter IV is a fantastic fighter, but can make you rage. 
if there's an absolute own, it's going to have to be Street Fighter IV and GTA IV for me.

" Everything! "

Ninja Gaiden Sigma 1 (but not #2),  Valkyria Chronicles, Demon's Souls.

Rachet and Clank games I just started the first one and they are a ton of fun.

Prince of Persia and Assassin's Creed (1 &2).

Not Borderland. Good god that game is just a mess. 

" @Kaz_Hooray said:

" Everything! "

You made an account to post on my blog? I am honored. "

Best bet is to return it immediately.

" @Emandudeguyperson said:

" @Kaz_Hooray said:

" Everything! "

You made an account to post on my blog? I am honored. "

Yeah, I'm your guardian angel
 
You should really look into this bundle "

" Best bet is to return it immediately. "

By the time I get a PS3, Sony's 10 year life cycle will be over. Life sucks, nothing but a dream killer.

Little Big Planet

I think you should look at Little Big Planet closely and see if its really for you.It can be sort of frustrating.

I wouldn't bother with the first motorstorm if i was you. Other than MGS, you should pick up...
 
Infamous
Valkyria Chronicles
Uncharted 1 and 2
Motorstorm: Pacific Rift 
Wipeout (Only available on PSN unless you live in Europe)
GTA 4
Ratchet and Clank (Whole series is good but just pick up the latest one if you're not sure)
Littlebigplanet  

And if you don't own them already, maybe some other multi platform games like...
 
Borderlands
MW2
Batman: AA
Both Assasins Creed games
Prince of Persia
Bioshock 
 
but you could already have those on another system for all i know.

I dunno if you played God of War I & II, if not get the GOW Collection.
 
A must own.

I would not bother getting  Motorstorm 1 as 2 is the same, just better.   These are the games I would recommend:

• Demon's Souls (action rpg - v. addictive)
  
• Uncharted 1+2
• inFamous (~£15 new)
  
• Valkyria Chronicles
• Ratchet and Clank series (get tools of destruction on the cheap first if your not sure)
• Trine
• Little Big Planet (can get it for <£10)
  

• Dirt 2
• Prince of Persia (Can get it for £10 new.  Not very hard but great story)
• Batman AA
• Borderlands
• MW2
• Saints Row 2 (ludicrously fun ~£10)
• Battlefield Bad Company (~£13)
  

I'd say rent U1 and buy U2.  I haven't played it on the PS3 (I hear it's bad) but you could try The Orange Box, too. If you don't have a PC, that is.
 
@yani said:

" I would not bother getting  Motorstorm 1 as 2 is the same, just better.   These are the games I would recommend:

• Demon's Souls (action rpg - v. addictive)
  
• Uncharted 1+2
• inFamous (~£15 new)
  
• Valkyria Chronicles
• Ratchet and Clank series (get tools of destruction on the cheap first if your not sure)
• Trine
• Little Big Planet (can get it for <£10)
  

Multiplat options

• Dirt 2
• Prince of Persia (Can get it for £10 new.  Not very hard but great story)
• Batman AA
• Borderlands
• MW2
• Saints Row 2 (ludicrously fun ~£10)
• Battlefield Bad Company (~£13)
  

"

" I dunno if you played God of War I & II, if not get the GOW Collection.  A must own. "

BATMAN! 
maybe modern warfare 2 if you have friends on ps3

If you like slower paced tactical JRPGs - Valkyria Chronicles is a must.
 
Almost all of the PS3 exclusives are actually worth the time and dime spent on them.
 
Just play them all.

Try out the LittleBigPlanet demo before you buy. I thought I'd really enjoy it, and it turned out to be only a so-so experience. That's just me, but regardless, try the demo first.

MGS4

definitely Uncharted 1 & 2. Besides that I guess I would recommend inFAMOUS. You already said the only PS3 exclusive games I have.