I've never really had any issues on my 360. That said, I got the GOTY edition of Oblivion from my Cuz. He had the first version, so he didn't want two disks.
And then with Fallout 3, I got that GOTY edition from a friend of mine. Those ran fine with the fixes they had. I did have one issue, but it was entirely my fault. It evolved vampires, and the mages quest, the thieves guild was mixed in there, and I had all ready finished the main quest...oh ya, the DarkBrotherhood was a problem starter as well. Ya know, its hard to find daedric hearts after finishing the main quest...
Anyway, the only real game I got that wasn't GOTY was NV. I got it...just after the first patch I think. It worked fine for me. No real issues. To be honest, the GOTY edition for Oblivion freezes up more often than NV does. NV only really freezes up when I've been playing to long.
I'm gonna get Skyrim, if not on 11-11-11, the weekend after. You know its going to be buggy as hell, TES is in the title.
But the support has gotten better for these things in my opinion. The game's going to at least be somewhat playable, and then the patches will come to make everything all better. Patching is a relativly new thing, and Oblivion came out with the new generation of consoles. Patches really weren't used that much before in the old generation. At least not automatic free ones. So we should be happy Skyrim's patches will be free, instead of having us go out and buy another disk that has a mix of dlc and patches.