@freon mass effect 1 was a 360 exclusive until 2012
dead rising 1
guitar hero 2, cod 2, and hitman blood money were next gen 360 exclusives

all of these above games are highly rated, were popular at the time, and are currently remembered as most influential/best games of all time. they also all released in the first few years of the 360's lifecycle.

for less impactful microsoft games: alan wake, fable ii, project gotham 3 and 4, crackdown, viva pinata
for niche games that are also excellent: ace combat 6, beautiful katamari, earth defense force 2017, blue dragon, and lost odyssey
also every xbla retro port which sony didnt allow on ps3 because the execs thought old games looked bad.