Over the years, there have been a lot of really bad fonts in games, especially English translations of Japanese RPGs.
First, what many refer to as the Tales of Symphonia font. It's awful, and it's used in a fair number of games, including...
Tales of Symphonia
Shadow Hearts
Romancing SaGa: Minstrel Song
Breath of Fire 4
Also mentioned is the DS devkit font, but without screenshots of it. So here's some:
Suikoden Tierkreis
Retro Game Challenge
Devil Survivor
999 uses the larger version of the font, so it's not as offensive, but still not good at all.
There are also some fairly crappy Japanese fonts, but one of them is particularly pervasive. Some examples:
Final Fantasy 12
Infinite Undiscovery
Ghost Trick - the English version actually uses the same font, which surprised me. The Roman letters don't look quite as bad, but it's still not very good at all.
As for examples of good typography, Square Enix actually had some great examples on the DS this past generation.
Final Fantasy Tactics A2
The World Ends With You
The IBM font that Atlus USA has been using recently is also quite nice.
Etrian Odyssey 3
Radiant Historia
In terms of Japanese fonts, there's actually a fair number of really good ones, but I think FF9 was the first time I ever saw a Japanese font in a game and thought it looked absolutely wonderful.
I feel like I could go on forever. I might make another post. I really want to give props to some other games like Ni no Kuni for its bold use of a slab serif (to great effect!) and a couple of other games.