Using Bitcoin contracts to run a betting site without the need for deposits? There are a couple of bitcoin betting sites, but they all seem to require making a deposit with them. Is it possible to somehow use the Bitcoin contract system to establish a distributed betting pool? Once the bet is decided one way or the other, the transactions would become active. 

The problem of course is who decides which side won. That could be the betting site operator. This way, you still have to trust them enough to make a fair judgement call, but at least they cannot just take everyone's deposits and run. The worst they can do is declare the wrong side of the pool the winner. Or maybe stay inactive, thereby locking funds (though this could be fixed by a decision deadline in the original contract).

Or this could be distributed as well. Maybe a majority of pool members gets to decide by some kind of voting process (requires fair losers). Or the block chain miners get to decide by including one of the two possible transactions into the block, just like they decide on double-spending right now?

Does any of this seem feasible (and meaningful)?
Giving the operator the power to control the identity of the recipient won't work, since he can participate himself and declare himself the winner. A majority vote also isn't too good because an attacker can make multiple entries, which is cheap to do if he knows he can guarantee a win.

It is necessary that the winner will be decided according to public data (such as the hash of a future block), and that the operator (or majority) will not be able to secure funds before sending payment to the agreed winner.

The only way I can think of is burn-escrow. Each participant sends a tentative payment to the operator which cannot be reversed, it can either be carried through or burned (with a deposit that incentivizes carrying through). Then the operator sends to the winner using his own funds. Then every participant forwards the payment. If the operator does not send to the winner, participants burn the payment and refuse to do business with the operator again.

There is some risk that the operator will be honest but participants will neglect to forward payments, or that the operator will be fraudulent but participants forward payments anyway to get the deposit. But with a properly calibrated deposit, these risks can be mitigated and entered into the pricing.