I recently discovered that SE 2.0 lets me put bounties on other user's questions, so I tried offering bounties on a few of the questions on math.SE which I thought shouldn't still be open. So far, one is answered and one remains unclaimed, so that's good.
When the question I put a bounty on was answered, I didn't get a notification in the universal mailbox. (Whatever you call that thing in the upper left of the screen.) It seems to me that it would be better behavior if I got notification for these questions, since I cared enough to spend rep on them. I realize that watching the bounties tab on my user page is an alternative, but not as convenient.