1) Xbox 360 (Crysis, Mass Effect, Lost Odyssey, Dead Space, Gears of War, Alan Wake, Skyrim, GTA4, Assassins Creed)
2) Playstation (Final Fantasy 7, Metal Gear Solid, Twisted Metal 3, Final Fantasy 8, Resident Evil 2)
3) Nintendo 64 (Goldeneye, Mario 64, Zelda: The Ocarina of Time, Mortal Kombat 4)
4) Xbox (Halo, Ninja Gaiden, Splinter Cell, Doom 3, Half-Life 2, Fable, Project Gotham Racing)
5) Dreamcast (Sonic Adventures, Soul Calibur, Skies of Arcadia, Grandia 2)

Never realized how many people here on VgChartz love the 360. It always seem to be a Sony/PS3 fan site. What I also notice is that most people who owned both 360/PS3 usually preferred the 360. I notice this with all my friends and family but I noticed it more on the internet also.

1 original xbox, 5 games lasted the entire console cycle without getting boring.
2 N64 mario party 1 is still one of the best games ever.
3 360, at first 360 was perfect but MS decided 3 years in the generation that kiddies are what play 360 not gamers.
4 PC starcraft/mmos
5 i want to say PS2... but after i got the xbox i basically threw the PS2 away since other then GTA xbox was better...

I love the 360 and i can see it being my first favorite console of all time. But mostly thanks to multiplatform games.

Although I wouldn't really say its most people, I think a lot of it has to do with most Americans getting the 360 as their first console and ps3 later on to supplement it. For example I relate Dragon Age, bioshock, oblivion, fallout 3, and borderlands with my 360 simply because I only had a 360 when those games came out. So thus I've had a better experience with my 360 simply because my favorite games this gen, despite being multiplatform, were played on my xbox. 

Not including handhelds or the PC:
1. PS2
2. Genesis
3. SNES
4. 2600
5. NES
6. Dreamcast
7. GameCube
8. Xbox
9. PS3
10. 360

For me the Xbox 360 is number 2. Mainly because I'm a very nostalgic person and even though Mass Effect and Halo are my current favorites series, the Dreamcast holds a very special place in my personal gaming history. I'm going to do a top 10. If you don't like that consider the latter five to be honorable mentions.

1. Sega Dreamcast (Shenmue 1&2, Crazy Taxi 1&2, Rez, Skies of Arcadia, Resident Evil 2,3, & Code: Veronica, Sonic Adventure 1&2,, Sega GT, Test Drive Le Manns, Looney Tunes Space Race, Grandia 2, Headhunter, Ikaruga, Stupid Invaders, Sega Rally 2, House of the Dead 2, Episode I Racer...)

2. Xbox 360 (Mass Effect 1,2,&3, Halo 3, ODST, Reach, Anniversary , Gears of War 1,2,&3, Left 4 Dead 1&2, Forza 4, PGR4, Portal 1&2, Tomb Raider Legends,Anniversary, MGS HD Collection, Alan Wake, Need for Speed Hot Pursuit, Ridge Racer 6, Enslaved, Majin, Fable II....)

3. Nintendo 64 (Zelda OoT, Super Mario 64, Shadows of the Empire, Rogue Squadron, Top Gear Rally, Star Fox 64, Mario Kart 64, Jet Force Gemini, Wave Race 64, Pilot Wings 64,...)

4. Saturn (Panzer Dragoon Saga, Panzer Dragoon II Zwie, Panzer Dragoon, Burning Rangers, Resident Evil, Magic Knight Rayearth, Radiant Silvergun, Thunder Force 5, Sega Rally, Shinning Force 3, Wipeout, Need for Speed....)

5. Xbox (Halo 1&2, Panzer Dragoon Orta, Tron 2.0, MechAssault, Armed & Dangerous, Beyond Good & Evil, Star Wars KOTOR, Doom 3, Half-life 2, Outrun 2006: Coast 2 Coast, Need for Speed: Hot Pursuit 2...)

6. Playstation (Metal Gear Solid, Final Fantasy VII, Ridge Racer Type 4, Rage Racer, Klonoa, Crash Bandicoot, Jet Moto 1&2, Mega Man Legends,, Need for Speed High Stakes, Need for Speed 3, Colony Wars...)

7. Sega Genesis/CD/32X (Sonic 1,2,3,Knuckles,&CD, Virtua Racing Deluxe, Virtua Fighter, Star Wars Arcade, Popful Mail, Phantasy Star IV, Lunar 1&2, Snatcher, Outrun, Top Gear 2, Contra: Hard Corps, Castlevania Bloodlines...)

8. SNES (Star Fox, Pilot Wings, Super Mario World, Allstars, Doom, Zelda A Link to the Past, F-Zero, Chrono Trigger, Mega Man X, Mario Kart...)

9. Gamecube (Metroid Prime 1&2, Mario Kart DD, Zelda TP, Mario Sunshine, MGS Twin Snakes, Star Fox Assault, Wave Race Blue Storm, F-Zero GX...)

10. NES (Super Mario 1,2,&3, Castlevania 1&3, Mega Man 2, Donkey Kong 1&Jr., Kirby's Adventure, TMNT 2&3, Contra, Super C, Shatterhand...)

And my favorite handhelds are:

1. Gameboy (Mario Land 1,2,3, Tetris, Castlevania, Operation C...)

2. Nintendo DS (New Super Mario Bros., Zelda PH, Zelda ST, Ridge Racer,)

3. Gameboy Advance (Super Mario Advance 1,2, Zelda MC)

4. Game Gear (Sonic 1,2, Triple Trouble, Columns)

5. Neo Geo Pocket Color (Sonic Pocket, Metal Slug, Puyo Pop, Bubble Bobble)

4th behind the SNES, Wii, and PS1.
It's got a lot of great games, and has the best multiplats most of the time, but its unreliability is a real pain, and it does lend itself to the "cinematic presentation over gameplay" trend that I hate about this gen.

1 - PS2
2 - PS1
3 - PS3
4 - N64
5 - SNES
6 - NES
7 - PSP
8 - DS
9 - Xbox 360
10 - Wii
By the way, these 10 consoles are all the consoles that I've ever owned (except the NES, which I played on an emulator).

you know, I think the next xbox will be better since MS made a lot of improvements with the 360 over the original, it's just a shame that it will never make it in my fav category due to XBL. Oh and I've never had RRoD when I had it, for the unfortunate souls that ran into that issue, my condolences and shit. /point and laugh