These are the 5 top bass rigs according to Wired2Fish. While I don't totally agree that these are the only five you need to know, they're definitely five worth learning about!
I've typed up some more detailed info about each rig so that you can actually learn how to use them as well; follow the links to learn more:
1. Texas Rig - http://www.vingle.net/posts/317866
First learned, basically second nature rig for hooking up plastic worms. A must know for all conditions! Perfect for grass, rocks, brush, timber and manmade structures.
2. Carolina Rig - http://www.vingle.net/posts/317874
Looks more natural because the weight is away from the worm, so as you pull the weight along the bottom the worm will dance and dart and suspend momentarily behind the weight. Great for feeling the bottom.
3. Drop Shot Rig - http://www.vingle.net/posts/328575
Great way to fish vertically. You can fish it vertically in cover or make casts to deep structure and work it back slowly like a texas rig until you contact a piece of cover.
4. Wacky Rig - http://www.vingle.net/posts/332261
This is a great technique in clear water. The fish need to be able to see the worm but it looks very lifelike. You can fish it around floating cover like docks or around bedding bass or bass relating to vertical structures.
5. Neko Rig - http://www.vingle.net/posts/335633
It’s the exact opposite of a wacky rig because of how the worm is displayed to the fish. Where a drop shot is a horizontal presentation mostly fished vertically, the Neko rig is a vertical presentation fished horizontally.