This has recently become much more straightforward with the command svndumpfilter. Details are available in the subversion documentation here. Basically, to avoid conflicts (explained here), it takes a repo dump and redoes each commit, either including or excluding a given file prefix. Basic syntax:
svndumpfilter exclude yourfileprefix < yourdump > yournewdump
Exclude is probably what the question asker is looking for, but you can also use include to, say, extract a subtree of the repo so as to spin it off as its own repository.
The latest revision of subversion in subversion (very meta) can also take glob patterns. I recently had to remove all pdfs from a repo and it was very easily done like so:
svndumpfilter exclude --pattern '*.pdf' < dump > dump_nopdfs
Further usage information can be found by calling svndumpfilter help and svndumpfilter help exclude.