The Minecraft community has created dozens of programs that can be used to enhance the game. Server software is so numerous that it has a page of its own. The most popular programs are Mappers that create an overhead view of a level. Map Editors let you directly alter a level outside of the game. Terrain Generators create new terrain types that aren't available normally. Finally, there are Specialized Programs for editing your inventory, simulating Redstone circuits, and altering game files at a low level.
Mappers
Infdev Map Visualizer
Created by Notch. Official site. Alpha only.
Isocraft
Forum thread. Classic only.
Cartograph
Forum thread. Alpha only.
pynemap
Forum thread. Alpha only.
Minecraft Topological Survey
Forum thread. Alpha only.
Map Editors
Omen
Forum thread. Classic only.
NBT Forge
Forum thread. Alpha only.
MCEdit
MineEdit
All-in-one Editor. Forum thread. Alpha only.
LolEditor
Forum thread. Alpha only.
Terrain Generators
ZOMG
Forum thread. Classic only.
MCMapper
A dungeon generator. Forum thread. Alpha only.
Specialized Programs
INVEdit
Forum thread. Alpha only.
Redstone Simulator
Forum thread. Alpha only.
NBTEdit
Forum thread. Alpha only.