For me, these are my "must own" 360 games:

1. Oblivion
2. Saint's Row
3. Gears of War

For the XBLA, my favorites are:

1. Worms
2. Geometry Wars

Dead Rising
Fight Night R3
Gears of War
Dead or Alive 4
Condemned

Guitar Hero 2
Crackdown
Dead Rising
Lego Star Wars 2
(enter your favorite sport title here)

Gears
Guitar Hero 2
Oblivion
Crackdown
?????

Those are the 4 I'd buy right away if I were picking up a 360..as is not enough yet for $400 when I can just play at my friends. Well, I probably wouldn't get GH since I have the PS2 version, but if you don't it's a must buy.

For the 360...

Gears of War
Rainbow Six: Las Vegas
Guitar Hero 2
Castlevania: Symphony of the Night
Worms
Zuma (*ducks*)
Assault Heroes
Geometry Wars
Dead Rising
Crackdown
Splinter Cell: Double Agent (Xbox edition)
FEAR

Crackdown
Viva Pinata
GoW
Dead Rising (do not own yet, played at friends')
Burnout Revenge

XBL
Geometry Wars
Uno
Worms

I'm holding off on dead rising because i heard a rumor that the GH version will include live co-op. (co-op will also be available via download for a small fee) I can wait for now, I have lots of games to keep me busy.

Why the duck, I thought Zuma was a lot of fun.

360 in no particular order
Crackdown
Kameo
Gears of War
Condemned
Burnout Revenge

XBLA
Zuma
Castlevania Symphony of the Night
Worms
TMNT

I still have a lot of big games that I haven't played like Dead Rising.

Current: Call of Duty 2
Crackdown
Gears of War
Oblivion

Arcade: Assault Heroes
Castlevania
Geometry Wars

Future: Bioshock
Half Life II Orange
Too Human