Ehm, I wonder a bit, the discussions always goes that HTML is not regular. The poster though asked to just match any open tags. The language of HTML tags clearly is regular, isn't it?
<!DOCTYPE html>
<html>
<head>
<title>I AM YOUR DOCUMENT TITLE REPLACE ME</title>
</head>
<body>
<div>
<br id="<bl>">
</div>
</body>
</html> <br id="<br id="<br>">">
Anything that requires balanced matching is NOT parseable with standard Regular Expressions, and by not parseable I mean that you will literally have an infinite amount of bugs. Shoot me an email and I can show you the math.
Even with Perl's whiz-bang recursive not-really-regexes-regexes, it's strongly not recommended to tackle balanced matching problems like HTML or XML. It might be theoretically possible (I haven't actually checked), but your brain will leak from your ears and you probably won't get it right, no matter how smart you are.
If it was XML, one might get in trouble with "<[CDATA[" sections, but regarding HTML, I don't see a real issue here.
... especially not from the pragmatic point of view. Depending on the use case and the quality of the HTML source, a "dirty" regex hack might be a far better solution and using a DOM parser.