I have both consoles, completely prefer the Sony brand through out though wouldn't use the term fanboy, too level headed. However this is what I use/used (don't turn it on much anymore) my 360 for:
At first, a decent party chat. However since getting my PSP GO, we all simply Skype. Much easier. So I can securely take that one off of the list.
As a Biohazard fan, DEAD RISING hit home and seeing as it never came to the PS3 (or any console in a good form), it gave the system some worth.
Until now, finally... the 360 was home to all of the RPG's I wanted to play. Luckily that trend is now dying, but it still has some points for ToV in my book.
Fighters. Yes, the controller sucks, but I have two arcade sticks and never play fighters on a controller anyway. The net coding seems better, I encounter less drops/lag and some of the games (MvC2) came out earlier and run better. Being a big fighter fan, this at least makes me turn on the console. Also, the only Virtua Fighter we have online. Version C or not...
PGR4. Was a huge PGR2 fan, PGR3 was decent and PGR4 brought it home again. For me at least.
Left4Dead series. Plain and simp, though I could play it on PC...
BIOHAZARD 5, it's superior on the 360 if I like it or not and Biohazard is my middle name. Not to mention there was a Biohazard LE console (US), so it won a few brownie points from me there.
I suppose I can list HALO 2 (played Halo 3 a bit, hated the MP. Inferior in every way to H2). While it was still popular I played it through B/C, though now I play on Vista.
Backwards Compatability. Mainly the Fatal Frame gams, the look and run fantastic on the 360. I'd own the console just for this.
So those are my reasons to turn on the console, however I have a ton more for the PS3, the 360 proves to have some worth in my collection. Ironically it's not for the typical games that people buy a 360 for, but that just shows their direction is little more broad now.