Really, the tone of the campaign has a huge impact on how acceptable or unacceptable this sort of stuff is. In a low-magic, dark age-style and/or 'every man for himself' heavy roleplaying campaign, this kind of behavior is almost to be expected. It can be a drag, but the best way to deal with it, imho, is in-character. When the other pcs find out about it, are they going to keep traveling with him or kick him to the curb? Or kill him??
Starglim said:
...you are justified as a DM in maintaining fairness and good feeling by (a) disallowing the action, (b) if you don't disallow it, favouring the other players in your game ruling by letting their characters detect and react to it, and (c) refusing to give him an in-game reward for it. You could tell him up front that all items that he steals from the party will prove to be non-magical and worthless.
I have to say that I completely disagree with Starglim here (no offense). If he steals the ring that the bad guy used to spray flames all over the party, it ought to be able to keep sprayin' flames (unless it's out of charges or something). As to just 'disallowing' it, it's one thing to approach this out of game and
ask the player not to do it, but I'm a dm of several decades who is all about keeping a firm hand on the campaign's details, but
no way would I ever tell a player what he could or couldn't do with his own character. That's not what the dm's for, imho.
But again, it depends on the style and tone of the campaign. And again, all this is just my personal feeling on the subject. But then again, I have no problem with pcs killin' each other, and I have no issues whatsoever with killing the pcs myself (and almost none about inflicting a tpk).