Two formats are currently in use: PNG and TGA. I started with PNG (some of the oldest graphics are in this format) and later got used to TGA (because a friend told me it has a better compression - I don't bother if it's true...). You are free to use any of these. From serious reasons you can use even other formats, the only condition is that RUDL library can load them (see RUDL Documentation).

For tilesets (Chapter 7, Tilesets) there is just one standard format, PNG, because the supported map editor, Tiled, accepts only PNGs.