(Windows) Exception Handling: to Event Log or to Database?

You need to differentiate between logging and tracing. While the lines are a bit fuzzy, I tend to think of logging as "non developer stuff". Things like unhandled exceptions, corrupt files, etc. These are definitely not normal, and should be a very infrequent problem.

One thing that needs considering about event logging is that there are products out there which can monitor your servers' event logs (like Microsoft Operations Manager) and intelligently do notification, and gather statistics on their contents.