Can I defeat an opponent with their own commander?
Yes, you can make a player lose by dealing 21 total damage to them with their own commander. (If it keeps getting stolen by yourself or others, a cumulative total 21 damage from their own commander will make them lose.)

The rule, from mtgcommander.net's Rules &mdash; Play section, is:


  
  If a player has been dealt 21 points of combat damage by a particular Commander during the game, that player loses a game.
  


That is any one specific commander card, including their own. Commander damage from different commander cards doesn't count together: if you've successfully stolen every commander on the board and dealt 20 damage with each of them to one opponent, they still haven't lost to commander damage.

Also, commander damage never makes anyone win directly, it only makes players lose. You'll only win if them losing made you win, e.g. they were your only opponent.