Somebody always posts this comment re: Computer Modern, but I've never seen anybody offer up some of these strictly superior printing fonts (of which there are apparently many). Would you care to link some examples?
I prefer Palatino when typesetting mathematics using latex. It looks nicer than Computer Modern and is super easy to use. Nowadays I use xelatex and actual fonts instead of staying stuck in the tex font ghetto.
The main problem isn't supporting other text fonts (including TTF), but the fact that those fonts don't properly support the symbols.
So all in all it's a bit of a nasty aesthetic trade-off. There are several packages that attempt to create symbol sets to match things like palatino, with varying success. Some are just terrible. And there are a few commercially available ones that do support most if not all symbols, so if it's worth a few hundred dollars to you there is that route.
Nothing has great solution for web, really. We're slowing moving from execrable to ugly but at least it is progress.
http://www.tug.dk/FontCatalogue/palatino/