You know, given the fact that I'm what many people call "young", I've heard too much criticism about RegEx. You know, "he had a problem and tried to use regex, now he has two problems".
Seriously, I don't get it. It is a tool like any other. If you need a simple website with some text, you don't need PHP/ASP.NET/STG44. Still, no discussion on whether any of those should be avoided. How odd.
In my experience, RegEx is probably the most useful tool I've ever encountered as a developer. It's the most useful tool when it comes to #1 security issue: parsing user input. I has saved me hours if not days of coding and creating potentially buggy (read: crappy) code.
With modern CPUs, I don't see what's the performance issue here. I'm quite willing to sacrifice some cycles for some quality and security. (It's not always the case, though, but I think those cases are rare.)
Still, RegEx is very powerful. With great power, comes great responsibility. It doesn't mean you'll use it whenever you can. Only where it's power is worth using.
As someone mentioned above, HTML parsing with RegEx is like a Russian roulette with a fully loaded gun. Don't overdo anything, RegEx included.