Game Specific
If you'd like to hack a game, but lacks the knowledge to do so (not to mention the time/interest to learn how), chances are that a custom written program for that particular game exists.
Of course, using these tools won't make you a better romhacker. Also, there should already be about 100+ hacks of the same game floating around the net, since you're probably not the first one who have tried programs like these out.
These are only a few of the existing programs available, and romhacks.net doesn't claim copyright or authorship to any of them.
Snes
Final fantasy 3 Multi Editor - Monsters, spells and more . By Lord J
Hyrule Magic - General editor for The Legend of Zelda: A Link to the Past. By Dragoneyestudios.
Lunar Magic - General editor for Super Mario World. By Fusoya.
Shampoo - Level editor for Bust-a-Move. By Dragoneyestudios.
Nes
Bubble Bobble Level Editor - The name says it all
FFhackster - Edits text, maps and lots of other stuff. By Disch (Slick Productions).
Rock and Roll - Edit levels, attributes and more in Mega Man 1. By Dan.
SMB Utility - Editor for Super Mario Bros 1, levels, enemies and more. By the SMB Laboratory.