Your mostly out of luck with a none-Symbian Nokia like the 6600 or 3650. There are some pretty decent emus for Symbian phones. The commercial vBoy, now version 1.3 I guess, plays Gameboy games full speed with sound and due to the very small resolution of the Gameboy that even fits the Symbian screen's resolution, it is quite a pleasant experience. I played the Oracle games on my 6630. Really enjoyable.
vNes plays the NES full speed, full sound, but due to the limited resolution, cropped badly.
vSun, even though it is a commercial product, is slow but at least reasonably compatible. I wouldn't recommend it though.
PicoDrive brings really great Mega Drive emulation to Symbian phones, but they are, as always, cropped.
And then there's Mame, or for my phone (6630) EEMame. It's great for the golden age games, cropped or not. Dig Dug rules, also Frogger and Galaga. No NeoGeo or CPS 1 though.
On the Java side you won't get that much diversity. Yet there are some remakes of classic arcade games. I've seen King of Dragons (2?!?), Pacman, Frogger, even some Mario clone, but I haven't tested most on them.