For headers I love using Myriad for professional things. I guess it showed up when I installed Photoshop. Although, I can't use it in flash, only in Adobe Products. (Even though now Flash is actually a Adobe Product)
But I like to mix it up, change it according to theme. Like for the The Peeps' Website, I used more stencil and grunge fonts to fit the theme. (The peeps is my brother's band. )

For HTML I mainly use Verdana, especially "tech" sites. Tahoma rarely.
I'm trying to use Lucida Sans, like hicksdesign. But I haven't checked the CSS yet for the exact name of the font yet.
Trebuchet MS is a nice one, I usually use it for headers.
I never, by any circumstances, I use Times New Roman in HTML, only in a fallback.

I get my fonts from http://www.dafont.com