We used a Log Database at my last job, and it was great.
We had stored procedures that would spit out overviews of general system health for different metrics that I could load from a web page. We could also quickly spit out a trace for a given app over a given period, and if I wanted it was easy to get that as a text file, if you really just like grep-ing files.
To ensure the logging system does not itself become a problem, there is of course a common code framework we used among different apps that handled writing to the log table. Part of that framework included also logging to a file, in case the problem is with the database itself, and part of it involves cycling the logs. As for the space issues, the log database is on a different backup schedule, and it's really not an issue. Space (not-backed-up) is cheap.
I think that addresses most of the concerns expressed elsewhere. It's all a matter of implementation. But if I stopped here it would still be a case of "not much worse", and that's a bad reason to go the trouble of setting up DB logging. What I liked about this is that it allowed us to do some new things that would be much harder to do with flat files.
There were four main improvements over files. The first is the system overviews I've already mentioned. The second, and imo most important, was a check to see if any app was missing messages where we would normally expect to find them. That kind of thing is near-impossible to spot in traditional file logging unless you spend a lot of time each day reviewing mind-numbing logs for apps that just tell you everything's okay 99% of the time. It's amazing how freeing the view to show missing log entries is. Most days we didn't need to look at most of the log files at all... something that would be dangerous and irresponsible without the database.
That brings up the third improvement. We generated a single daily status e-mail, and it was the only thing we needed to review on days that everything ran normally. The e-mail included showed errors and warnings. Missing logs were re-logged as warning by the same db job that sends the e-mail, and missing the e-mail was a big deal. We could send forward a particular log message to our bug tracker with one click, right from within the daily e-mail (it was html-formatted, pulled data from a web app).
The final improvement was that if we did want to follow a specific app more closely, say after making a change, we could subscribe to an RSS feed for that specific application until we were satisfied. It's harder to do that from a text file.
Where I'm at now, we rely a lot more on third party tools and their logging abilities, and that means going back to a lot more manual review. I really miss the DB, and I'm contemplated writing a tool to read those logs and re-log them into a DB to get these abilities back.
Again, we did this with text files as a fallback, and it's the new abilities that really make the database worthwhile. If all you're gonna do is write to a DB and try to use it the same way you did the old text files, it adds unnecessary complexity and you may as well just use the old text files. It's the ability to build out the system for new features that makes it worthwhile.