The Prediction game module (which has an official D7 version ...) seems like a great fit for this in a Drupal (version 7) site. There is also the Betting system module (which only has a DEV version for Drupal 6 ...).
Some details about the Prediction game module (from its project page, in which I added the bold markup here):
The Prediction game module lets administrators create leagues or tournaments consisting of several matches, on which bets by players can be made. After each round of matches, the results can be entered and players receive a certain number of points for their bets, depending (of course) on their accuracy.
A score board and practical interfaces for betting and for entering results are provided, multiple simultaneous leagues are supported. One current drawback is that matches of one round have to start all at the same time to be well accessible, but otherwise the module works pretty well.
Here is a screenprint of it (from its project page):
To get you going with it, refer to its README.txt, which includes this:
After enabling the module, go to "Administration » Content » Prediction games » Teams
" and create some teams. Then, you can create one or more competitions on which people can then bet.
After creating a new competition, you should probably put a link to it somewhere on your site (e.g., in some menu), so users will find it.
Remarks:
I don't think the Sports Pickem module (which has an official version for both D6 and D7) support betting "out of the box". Though it might be a possible alternative also to start from (and add bets-specific functionality yourself).
There is also the (active) issue "Merge with Tournament module", which contains this suggestion related to the Tournament module (which has an official D7 version):
Betting would be a great sub module for the new Tournament module or integrate with it in some way?
Here is a screenprint of it (from its project page):