I've played New Vegas for about 9 hours now (have a newborn at home so playtime is limited) on the Xbox 360 this time.
I haven't had a freeze yet (knocks on wood) or a corrupt saves, I do save often (a habit from Fallout 3 on PS3), only auto-save on sleep. I also take my time in areas looting and just looking around.
Only glitches I've had were: animals and NPC enemies falling into the ground; some out of sync talking and animation (Nash in Primm); using ironsights seems to make your gun move above your head but holstering your gun and switch to third person and back seems to fix it right away (they should patch that soon).
I've finished up a bunch of quests and haven't had a problem entering any towns. I still haven't made it to New Vegas, still in Novac.
I'm really enjoying this game, it is a lot different than Fallout 3, it seems more hostile and I know it was bashed in the reviews that travelling was boring cause of nothing around, but that's what a wasteland should be and it's nice to venture out and not have to always shoot something.
I do hope Bethesda/Obsidian keep patching this game and not drop it so fast like Bethesda did with Fallout 3.
Well in a nutshell, I haven't had many issues, and it's a lot of fun so far.
P.S. Here's my technical info: Xbox 360 Slim (250HD) with the game installed on harddrive and the classic pack DLC installed.