Should I use Tahoma in webdesign? If I couldn't opt for anything different (i.e. because the designer used it in his design), with which fonts could I make an stack of replacement fonts in a CSS stylesheet?
Tahoma's fine. Good replacements are Geneva and Verdana, with a generic sans-serif for backup. Better CSS Font Stacks is a great resource for suggesting these kinds of things.
If you're working with a designer who wants to use certain fonts, make sure s/he understands that very few fonts are web-safe sooner rather than later. It'll save you from some headache down the road.