Malkamaniac, can you tell me how valuable (if at all), knowing any of these programs is for a web designer: Photoshop, Illustrator, InDesign, and Corel Painter? I'm developing a course to teach and I can include any or all of these programs. It's not meant to be geared to a specific profession, but it helps to know what would be good for a web designer to know. Flash and other programs would have to come later.
Photoshop is an wonderful knowledge to have for everything. It's a great basis for design whether if be graphic/web.
Illustrator - unless you're vectoring or you are doing specialized design for print, meh in terms of web. Same for InDesign.
The well rounded basis for all web designers anymore? CSS, Dreamweaver, Photoshop, hell even notepad. Also, if you're straight designing in photoshop and need to cut out a complete design, a small base of knowledge should be taught to use ImageReady.