Where would you write an error log file, say ErrorLog.txt, in Windows? Keep in mind the path would need to be open to basic users for file write permissions.

I know the eventlog is a possible location for writing errors, but does it work for "user" level permissions?

EDIT: I am targeting Windows 2003, but I was posing the question in such a way as to have a "General Guideline" for where to write error logs.
As for the EventLog, I have had issues before in an ASP.NET application where I wanted to log to the Windows event log, but I had security issues causing me heartache. (I do not recall the issues I had, but remember having them.)