Hm...no one ever recommends Kameo, Project Sylpheed or Halo Wars (I haven't played them yet as I'm busy with XBLA games at the moment, but those were the first 3 retail games I bought last week for the system).
360 shall be known as my strategy/building sim console: I already bought Halo Wars, RISK: Factions, Outpost Kaloki, Defense Grid, next ones will be Viva Pinata 2, Tropico 3, Toy Soldiers, Kingdom for Keflings.
If you're not interested in strategy or sim, here are two definite recommendations:
Rez HD (XBLA) and Psychonauts (Xbox original)
And listen to pearljammer, the wise man who not only likes David Bowie but also recommended the excellent HD remakes of my most favourite game ever: The Secret of Monkey Island 1 and 2 (available on XBLA/PSN/Steam/D2D)
Also, every 36o owner should make sure to keep this wonderful 2011 XBLA game on their radar: http://www.youtube.com/watch?v=DmSAQwbbig8
