Having little or no space available in tempdb could cause problems for your applications. SQL Server uses tempdb as a workspace while performing queries. Large sort operations, server-side cursors, temporary object all make use of tempdb.
If your tempdb database is always full, there may be an issue with one of your application creating temporary objects but not dropping them. Although I would expect that you would only see this if you had an app that maintained a connection over a long period of time.
The easiest way to clear tempdb is to bounce the server. When SQL Server starts, it rebuilds the tempdb database (this is one of the reasons that noone backs-up tempdb). If tempdb is constantly running out of space, that's a clear signal that you need to increase the size. Check the SQL Server BOL for this information. It's a very easy process using the Server Enterprise Manager.
One other note, you didn't say which version of SQL Server that you're using. 7.0 should default to expanding the database automatically. If this is the case, you're probably running out of space on the disk partition that tempdb is on.
-Mike