I know HTML, what else do I need to know?
For a developer: HTML, CSS, JavaScript, at least some ASP (with VBScript or JavaScript), at least some PHP, SQL, Perl would be nice, and be proficient in hand-coding these. Knowing the arse-end from the elbow of IIS and Apache would also be a bonus, including modifying the server configuration. Knowing that FrontPage X is crap is essential. The ability to source solutions, rather than spend hours writing code, is handy (why spend three hours writing DHTML menus when a $65 piece of software can get the job done in 15 minutes?) Someone who knows what they know and knows what they don't, ie. someone who truly knows.
For a designer: Flash, DreamWeaver, FireWorks (or Xara X), PhotoShop, Director (including scripting would be nice). Some mark-up ability would be useful, though an understanding of what you should/can and shouldn't/cannot do with a web page is essential. On the other hand, I'd expect you to push the developers' skills; make them think "Well, no, that can't be done" and have them come back an hour later with a solution. A skill in illustration is good.