Updating to OS X 10.10.3 (from 10.10.2), the process seemed to hang during the screen that said "restarting" (which comes after the screens that tell you how much time is left.)

A quick google showed that the right thing to do when the timer wasn't moving was to simply wait. So I just waited. About a half hour later, the process completed just fine.

So if your update process is seemingly stuck: just wait. Even if it takes a few hours for some reason, waiting it out will almost certainly be better than hard resetting a computer during an update process.