The OP doesn't seem to say what he needs to do with the tags. For example, does he need to extract inner text, or just examine the tags?
I'm firmly in the camp that says a regular expression is not the be-all, end-all text parser. I've written a large amount of text-parsing code including this code to parse HTML tags.
While it's true I'm not all that great with regular expressions, I consider regular expressions just too rigid and hard to maintain for this sort of parsing.