There are several issues here. Also, from your post it's not clear whether you intend to just reference the fonts in your app, package them with your app or display text in images that were produced with the fonts.
It is legal to use a font that's already installed on the user's system. That's why there's no issue with Arial, Times, etc. You are not redistributing them with your app.
When you redistribute a font with your app then you have to worry about licensing. Read the license carefully.
There are free fonts. These are available in various places under various free licenses. A little Googling turns up various pages with promising-looking free fonts.
You might look at the free fonts distributed with XFree86. They aren't as high-quality as the commercial fonts, though.
