I'm planning to play Oblivion for the first time but I'm not sure which version I should get. And the reason is, I've seen someone mention there is a quest which is bugged in the GOTY version.

But I can't remember what quest that is.

Can someone confirm if there really are GOTY version exclusive bugs?

The only thing like that I'm aware of is exclusive to the PS3 GOTY (English) version - the Vampire Cure quest is broken. But as long as you're aware of the bug it's no big deal. Just make sure you monitor your active effects tab and cure any active diseases...unless you want to be a vampire. If you're playing on xbox I know of no such bugs. Same if you're on PC, in which case you can also get the unofficial patches which fix even more (usually non-game-breaking) bugs.