Nintendo and HAL planned a sequel for Earthbound, a 3D game called Earthbound 64, but it was canned.
However, a sequel did come around in 2005, I think. It was creatively entitled Mother 3, a GBA game in the same sort of style of Mother 2 (Earthbound). The main character, Lucas, appeared in Smash Bros Brawl on the Wii; despite Mother 3 being a Japan exclusive.
The game is brilliant, and had a strong cult following. Due to this, it recieved a complete fan translation that was released in 2007, they worked really hard to translate thousands of lines of text over a 2 year period, and they did a good job too. If you can track down a ROM and the translation patch (shouldn't be too hard), I would highly recommend it.
Mother 2/Earthbound and Mother 3 are light-hearted JRPGs on the SNES and GBA respectively.
EDIT: I don't condone piracy. Unless it's the only way (like this!).
EDIT 2: I bookmarked this thread. Some interesting shit.