<p>Ok, so at some point in time, somebody checked in some files with names that require a case sensitive file system into the trunk of a repository that I constantly check out.  This of course leads to my local working copy locking up when I try to check it out (on my Windows computer).  Is there any way that I can set my local subversion copy so that it will ignore any files whose names differ only in case?</p>

You can use the repository browser to remove/rename the offending file then update your working copy as per normal, fix up any references to the file you renamed that may need fixing up, and commit the fixes.
Then drag up a shotgun and shoot whoever did this in the first place. Case sensitivity abuse is one of the few bad smells that I have trouble forgiving.
(edit: This assumes TortoiseSVN, but the solutions work for any SVN implementation. You just don't get to use a pretty browser.)
Edit:
The other option is to rename the local version of the file, then use the repository browser to check out the second version of the clashing files, move things around, sort out references as above, then commit the changes.
This has the advantage of only requiring one commit, and not messing around with other people unnecessarily who may or may not be working with the two files.