In Java I would do something like:
java.awt.GraphicsEnvironment ge =
java.awt.GraphicsEnvironment.getLocalGraphicsEnvironment();
Font[
Taken from Mark Murphy's answer on the Android Developers mailing list:
http://developer.android.com/reference/android/graphics/Typeface.html
There are only three fonts: normal (Droid Sans), serif (Droid Serif), and monospace (Droid Sans Mono).
While there may be additional fonts buried in WebKit somewhere, they appear to be inaccessible to developers outside of WebKit. :-(
The only other fonts are any TrueType ones you bundle with your application.
Edit: Roboto is a new font which came in with Android 4.0. You can use this library project to use it in all versions back to API level 4 https://github.com/mcalliph/roboto-text-view
Android includes 3 base fonts, but unlike iOS, allow you to use just about any font you'd like. You can simply embed it with your app, instead of being limited to a preset list of fonts like Apple does (Apple doesn't allow font embedding). Pretty convenient.
Note that this is for Android itself, but web browsers (including the basic pre-installed Android web browser) does support all the standard HTML fonts.
Regarding the actual question, here is a way to create a list of all available fonts installed:
String path = "/system/fonts";
File file = new File(path);
File ff[] = file.listFiles();
Array ff[] will contain all the font files.
There are only 3 fonts available as part of android; normal (Droid Sans), serif (Droid Serif), and monospace (Droid Sans Mono).
Apps can include their own truetype fonts but can't install them for use by other apps.
couple of links about the fonts: