Original games don't use EPROMs. I heard most people use the 27CXXX series of EPROMs on NES carts, but very often rewiring is required. The only boards that are pin-compatible with EPROMs are NROM and CNROM.
The same is true for Flash ROMs, in case you're interested in them. I've used AT29CXXX chips sucessfully. I think FlashROMs are better because they can be erased by the EPROM programmer in seconds, as opposed to the several minutes of UV light EPROMs need.
As for the Genesis, I believe the same chips will work, but since it uses 16-bit chips you'll have to use 2 8-bit EPROMS to simulate 16-bit ones. However, I don't think you can find EPROMs larger than 1MB, so the most you'll be able to have is 2MB, unless use tricks to put more than 2 EPROMs there.
Do you know
this page? They talk about making carts for lots of systems, there should be something of your interest there.
EDIT: Man, the animations in that page give me headaches!!