Edit: tchrist has informed me that my original accusations about Perl\'s insecurity are unfounded. However, the question still stands.
I know that i
Regular expressions are a programming language. I don't think they're quite Turing-complete, but they're close enough that allowing your users to enter them into your web site IS allowing other people to run code on your server. QED, yes, it's a security hole.
You might be able to get away with allowing a subset of whatever regexp language you want to use, whitelist a particular set of constructs to make it a not-big-enough-to-sweat-over hole... other people have already mentioned the possible dooms of nesting and * . How much you're willing to let people load down your server is up to you. Personally, I'd be comfortable with letting 'em have one SQL "CONTAINS" statement and maybe a "BETWEEN()". :)