Is Tahoma's font safe for the web?

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.

It depends on what you mean by "safe".

If you mean that a majority of the users have the font, and that you can pick a reasonable alternative for the rest, then it's safe.

If you mean that everyone should be able to view the page exactly as you see it, then it's not safe. Actually no font is safe, except the default fonts in CSS. That's why you should always provide alternative fonts as backup, and always provide a default font as the last resort. Example:

font-family: Tahoma, Arial, Helvetica, sans-serif;

Note that even if the user has the Tahoma font, it will not always render exactly the same. The user can have different settings for font smoothing, which greatly affects how the font is rendered. There may also be slight differences in kerning and hinting for different versions of the same font.

If you need some text to look exactly the same all the time, the only option is to make an image out of it.

According to the Code Style Font Family Survey, Tahoma is available on about 98% of Windows and 74% of Macintosh systems.

Their Build Better CSS Font Stacks page lists common stacks organized by category. They also have a Font Stack Builder that tells you the likelihood of a visitor seeing a particular font in the stack.