In HTML I can make a checkmark with ✓ . Is there a corresponding X-mark?

A corresponding cross for ✓ ✓ would be ✗ ✗ I think (Dingbats).

✗

✗ 

✘

✘ 

✕

✕ 

✖

✖

Personally, I like to use named entities when they are available, because they make my HTML more readable. Because of that, I like to use ✓ for ✓ and ✗ for ✗. If you're not sure whether a named entity exists for the character you want, try the &what search site. It includes the name for each entity, if there is one.

As mentioned in the comments, ✓ and ✗ are not supported in HTML4, so you may be better off using the more cryptic ✓ and ✗ if you want to target the most browsers. The most definitive references I could find were on the W3C site: HTML4 and HTML5.