Sims Art Studio by Maxis. An easy-to-use program, makes one-tiled paintings. You can find it in the Get Cool Stuff -> Make Cool Stuff section.

Transmogrifier (TMOG for short). It's the program that's used to clone objects and export and import sprites. Don't forget to make up a magic cookie number - you can find a list of ones already claimed at Magic Cookie Group. (magic cookie numbers help prevent object id conflicts)

Sim Catergorizer or SE Object Manager (SimCat is free). These programs allow you to determine what catergories your objects will be in the game - for example, downtown, magic town, kitchen, plumbing, plants.

If you have Vacation or up installed, you will need a program that will fix the sprite colors so T-Mog can read them properly. You can use TransPatcher 2 or Sim Catergorizer (for Sim Cat, select an object, click edit, then click "T-Mog Fix")

You will also need...

A decent graphics program, like Paint Shop Pro, Photoshop or Photoshop Elements.