Oblivion keeps crashing to desktop while I'm running Xfire. Anyone know why it happens?

Just close Xfire, problem solved

Xfire is a utility to track and join online multiplayer games (kinda like gamespy). Oblivion is single player only (with the exception of a very unstable and limited mod in testing now). You should have little or no reason to have it running in the background. When playing ANY 3d intensive game, its always wise to shut off any background programs to free up resources and make the game run faster.

Tyhons right just close it out. Close everything else out as well when you play and youll probably notice better framerates and quicker load times. Three birds with one stone, cant beat that!

More than that Alicia, <3 Xfire, I actually pushed for it to be added to Neo here.

Applications such as Xfire, TeamSpeak, and Ventrilo are optimized to run alongside games and use as little resources as possible. On my old system, I played Oblivion with a load of processes in the background (including Xfire) and almost never CTDed. On my new system that I've spent hours optimizing with various registry and performance tweaks and keep as clean as possible, Oblivion CTDs all the time, even though explorer is the one process using the most memory (aside from the game). None of my hardware is overclocked, and closing all unneeded processors doesn't help either, I guess I'm just screwed

As for your problem, Oblivion can be rather disagreeable with something on someone's system and fine with it on another's, so I don't think there's any "fix" for it other than closing Xfire. Seems to be your only solution.