That depends on the individual font and how it is encoded, then decoded into a human-readible glyph.
The shapes of the glyphs in fonts cannot be copyrighted. If fonts could be copyrighted, then every printed text that was rendered in such a copyrighted font would be a derivative work.
However, the data files that encode fonts can be copyrighted. If you bundle a font with your app, you have to take care to comply with any license terms under which that font is published. If you buy a font for personal use from Adobe, you are not license to redistribute it. I'm sure Adobe is happy to allow for redistribution, but to get licensed for that, you'll need to pay them a lot of money.
Many of the technologies for translating the font data files into the rendered glyphs that you see on-screen are patented. That is not likely to be a problem for you on mobile devices, as the patent licensing is the responsibility of whoever is distributing the implementation of these font-rendering technologies. That's usually the handset vendors.
You will only need to obtain patent licenses if you yourself provide the code that translates a font's data file into a screen glyph. If you are using the type rendering engine that is built into your mobile device's operating system then you don't need to worry about the patents.
Note that source code is not considered to be an implementation of a patented technology. Google doesn't have to pay any fees or obtain any licenses to distribute the Android sources.
That's up to the device vendors, as program binaries ARE considered implementations that are subject to the patent laws. I suspect that many such vendors don't understand that, and that they all figure that Google has licensed all the patents that cover the Android codebase. That would be the case if they were licensing a mobile OS in binary form, but it's not the case when they are just getting source code.