How would I go about implementing/emulating the SNES’ Mode 7 in Java?
Mode7 covers several different effects. So which one are you after? Rotating some ground plane as in mario kart or f-zero?
Right now, I’m just after emulating the effect used in world maps for RPG’s (like Secret of Mana), so that would probably fall under the rotation part of it. An explanation of the other effects wouldn’t hurt though. 
Maybe you could just draw the screen to a BufferedImage prior to drawing it to the actual screen. Then you could enlarge whatever part of the BufferedImage you need and rotate it as necessary.
If I’m thinking of the right effect from Secret of Mana, it kind of looks like the screen just keeps zooming in and rotating faster and faster.
i started out doing something similiar a while back to get some basic texture mapping in some java2d apps. this tutorial is pretty good, though it involves pixel-by-pixel operations, so you might find it best to use MemoryImageSource or something
it seems geared towards ROM developers, but it explains some of the math that might help you
http://user.chem.tue.nl/jakvijn/tonc/mode7.htm
also note that he wrote a second page after that (which isnt immediately obvious), so don’t forget to check that also: http://user.chem.tue.nl/jakvijn/tonc/mode7ex.htm
“The Super NES console has eight modes, numbered from 0 to 7, for displaying background layers, the last one having a single background layer that can be scaled and rotated.”
It was also used for effects which looked like there is something rotating infront of some background. The background, however, was actually build out of sprites. (An example would be one of the Contra/Probotector boss fights.)