Uncharted series.... and Journey... both are PS exclusives.

Demon's Souls.
Ratchet & Clank series.
God Hand.

You're welcome.

So. You are so rich that you could buy a ps3 and a xbox without even looking if there are any games you would like. Why not buy all of them then.

Playstation +
Uncharted series
Infamous series
Ratchet & Clank series
Little Big Planet 2 (Includes the entire community from the first game but not the main story)
Tomb Raider series.

This is a fairly good list. Start at #1 and work backwards. Chrono Trigger is my personal favorite.

For PS1, I recommend Castlevania: Symphony of the Night.
For Nes, I recommend Super Mario Bros 2 and 3.
For GBA, I recommend Mother 3 more than anything else, but there are many great ones, like Advance Wars and Fire Emblem.

red dead red dead red dead, but you got it already so go play RED DEAD!!!!

God Of Warseries for PS3 (the first 2 were on ps2 but they are awesome regardless)

Gears of War for Xbox 360 the series gets better with each game i thought but i only played the trilogy not the newest one i heard was not as good.

casltevania lord of shadows is coming to steam next month so while its a great game on consolethat i recommened i would say wait for steam version if you can, its supposed to have a little extra content.

The Last of Us

Gears of War

Resistance

Killzone

Xenoblade Chronicles was a great game you might have missed.

Since you have a new PS3, i recommend you to play these games. Have in mind that i got mine on February 2012, if that helps:

• Ratchet & Clank Future: Tools Of Destruction & A Crack In Time (only if you have played the PS2 trilogy; if you didn't, then get the HD Collection).

• inFAMOUS Collection (which nets you inFAMOUS 1, inFAMOUS 2 with all DLC and inFAMOUS: Festival of Blood).

• God Of War Saga (it comes with 5 God Of War games: 1 & 2 HD, 3, Chains Of Olympus HD and Ghost Of Sparta HD. It DOESN'T come with GoW: Ascension, which came months ago).

• Uncharted series (you could get the Dual Pack -U1 & U2-, and U3 vía PS+ if you are interested on it. It's well praised because it excels on everything: music, gameplay, characters, set pieces, and even the dialogue).

• Metal Gear Solid Legacy (comes with all MGS games: the first one runs on the PSOne emulator, and it comes with MGS 4. It's nice if you are interested on playing MGS series, so you can jump in MGS V when it releases. It DOESN'T come with Metal Gear Rising: Revengeance.)

• Heavy Rain (pure awesomeness on a Blu-Ray disc, GET IT!. Play it, so you can see why you should be excited about Beyond: Two Souls).

• Catherine (PS3/X360. A challenging puzzle game that you will like from start to finish. I challenge you to not read or watch any guides!. One of the biggest surprises that you can get on gaming).

• Killzone Trilogy (The first game isn't as fun as the other two games. KZ3 boasts splitscreen co-op, nice graphics running at 30 fps and a great campaign with different places to visit. The story isn't a big part here, and the characters are forgettable; that's why the devs want to make up for it on KZ: Shadow Fall.)

• Vanquish (PS3/X360. A short game that ANYONE should play. Action game at it's finest).

• SSX (2012 - PS3/X360. Remember those glory days in which Tony Hawk games were the glory, doing tricks and grinds and stuff. Well, this game is kinda the same thing, but with snowboards!. SSX games were a nice brand of EA, and they made it back. Lots of mountains to ride, tricks, challenges and stuff. Don't miss this one.)

• LittleBigPlanet 2 (So much charm in it!).

• Final Fantasy XIII. Be careful with this one: it has a convoluted story and gameplay can get tiring after a big while.

Other games that didn't made the cut:

• Gran Turismo 5 is a nice game, but i would suggest you to pick up GT6 when it releases.

• PixelJunk games (PS3/PSP/PSVita) are fun to play, but they aren't well recepted. PJ Shooter, for me, it's the best of the bunch. PJ Eden is the only one that you can get on PC.

• PSASBR is a great fighting game like Super Smash Bros.. It's fun to play with friends and online, but it has MUCH LESS features and bonuses than SSBB. Still it's not a bad game, and it's recommendable, just have in mind that there is a better one already.

• Dante's Inferno (PS3/X360/PSP). It's a nice game, but not as awesome as God Of War.

EDIT: I haven't played some games yet, like Ni No Kuni, Resistance Trilogy (there's a trilogy, just like the Killzone one), so i can't comment on those.

Get the Collections/Trilogies, because they are cheaper and they come with all DLC available.

Nier

Infamous

Gears of War series, Forza series, Fable II, Uncharted Series

halo 3

Skyrim

The first game for Xbox I would buy is "The impossible game", this is the website, in case you dont find it. (currently on Greenlight here)

God of War Series, but pirate your PS3!!!!

A lot of good ones have been mentioned, GOW series, red dead redemption, Gears of war. All good bets for sure.

However, I think Asura's Wrath earns an honorable mention, fun game.

I was actually working on a game list as well. I am also including games that are not on steam.

PS3 (Will buy later this year / Early next year)

• God of war Collection
• Metal Gear Collection
• Little Big Planet
• Shadow of Colossus
• Ratchet and Clank collection
• Killzone
• Jak and Daxter collection
• Heavy Rain
• Resistance
• Heavenly Sword
• Uncharted
• The Last of Us

X360

• Gears of War Collection
• HALO Series
• Prey (Very hard to find on steam)
• The Darkness (not on Steam)
• Kinect Sports 1 + 2 (Great party game)
• Dance Central (If you're old enough, you'll know why this is on the list.)
• Crackdown

I'm interested to see the final list and what you decide to get.

EDIT: Just read through some of the comments and there are some valid points that I overlooked. OP isn't asking for only 360 and PS3 games, He's asking for everything. I recommend rephrasing this part: "So now I need some great games, that are only available on consoles (every console except the wii u and ofc xbox one and ps4)."

I cant tell if that was done on purpose to see who's paying attention or attack of bad grammar. Regardless, common sense says to recommend games for consoles you have and not those you don't have.

As for recomendations for other consoles:

PS2

• Katamari
• Sly Fox

XBOX

• Breakdown (best game on the system, very under rated)
• XIII
• Fuzion Frenzy
• Jurassic Park: OG
• Psi-Ops (this is for free now on pc)
• Second Sight
• Mech Assault 2
• Steel Battalion (if you can get it)
• Time Splitters
• Conker: Live & Reloaded
• Panzer Dragoon (You're welcome.)
• Metal Arms: Glitch in the System

PSX

• Crash Bandicoot
• FFVII
• Ehrgeiz (Play FFVII first, this game may contain spoilers)
• Chrono Cross (play CT first)
• Spyro

N64

• Super Smash Bros. (Best one in the series)
• Golden Eye

SNES

• Chrono Trigger

Thats all I got as a recommendation. I should work on my backlog and organize my top ten played games list.

Heavy Rain, Last of Us, God of War Series, Metal Gear Series, Uncharted Series, Red Dead Redemption, Castlevania Lords of Shadow, Ico/Shadow of the Colossus collection, Siren Blood Curse, Valkyria Chronicles, White Knight Chronicles, Yakuza Series, Ratchet and Clank, Infamous Series, Everybody's Golf 5, Catherine, Bayonetta, Journey, Enslaved, Ar tonelico Qoga: Knell of Ar Ciel..... and a lot more japanese games...
In Xbox, Gear of Wars, State of Decay, mmm i dont remember more for now... xD

Wii:

• Animal Crossing: City Folk
• Donkey Kong Country: Returns
• Fire Emblem: Radiant Dawn
• Fragile Dreams
• Kirby's Dream Collection
• Kirby's Epic Yarn
• Kirby's Return to Dream Land
• Klonoa
• MadWorld
• Metroid Prime Trilogy
• No More Heroes 2 (Get the first one on PS3)
• Pandora's Tower
• Pikmin 1/2
• Punch-Out
• Resident Evil 1/Zero
• Sin and Punishment: Star Successor
• Sonic Colors
• Super Smash Bros. Brawl
• The Last Story
• Trauma Center: New Blood/ Second Opinion/ Trauma Team
• Xenoblade Chronicles

It looks like everything else is mention in the comments. Make sure to pick up Lost Odyssey for the Xbox 360, it's created by the original Final Fantasy team. Also pick up Ni No Kuni, Valkyria Chronicles & Folklore for the PS3.

Have you considered getting playstation plus? My friend really likes it.

Spelunky for Xbox is good, lots of fun

The Last of Us looks insanely good. I was thinking about renting a ps3 just to play it but that will probably never happen :(

Many of the titles already listed are great. I would recommend the Uncharted series and Ratchet and Clank series as some of my favorites. Also a game I haven't seen mentioned is 3D Dot Game Heroes, this is a throwback of sorts to older Zelda like adventure games (if you like the old Legend of Zelda games you will like this). Here is a list of more ps3 exclusives for more ideas: PS3 Exclusives