I was testing various Android web browsers (but I think the stock one is fine) and noticed that the MS "web safe" fonts (Trebuchet, Verdana, Tahoma and the like) were displayed with substitute fonts. It took me quite some time to notice, which means that it is a minor annoyance.
Out of curiosity, I was wondering if there was an easy way (I'm not talking about rooting here) to install these fonts. A quick Google search did not help me.
You might be able to change fonts in the browser depending on your phone, whether it is rooted, and whether the phone supports changing the Core Fonts. If it does support changing the Core Fonts you will need to apply the fonts wrapped as an .apk (there are lots available) or do it manually (but I suspect that needs root).
There may be other explanations - but in Best font for Captivate? is one which though poorly written is a pretty good explanation.
There's no easy way to do this. Android ships with two fonts: Droid Sans and Droid Serif. They are used for, well, everything. In Ice Cream Sandwich, it also ships with Roboto, a grotesque font similar to Helvetica and Din.
This will become less and less of an issue in the future as design-conscious web developers are using @font-face and serving up the fonts they use.
Also, keep in mind, those fonts you name aren't free. They're "web safe" because they ship with Windows. They are commercial fonts owned by Microsoft.