Building the Rover

The book Building Robots with Lego Mindstorms, by Mario Ferrari, Giulio Ferrari, and Ralph Hempel.

Spin at about 4000 revolutions per minute.
Need to be geared down to provide the appropriate speed and power. It's not unusual to need gear reductions of 1:96 or more to get good performance for some rovers.
Tip for running three motors from two battery packs (from the 2007 Mars Marauders team): Place the wire for the third motor on an unused section of the battery box. When you want to control this motor, remove the existing wire and move the third motor wire onto the battery box terminal. When done, move both wires back to their original positions.

Large and small pistons are available. Use the large pistons for anything that is heavy or needs a lot of force to move.
Tubing diameter between the pump and the piston affects performance. Smaller diameter tubing creates less of an air reservoir inside the tubing, which makes the controls more responsive.
Tip for running two pistons from one pump (from the 2007 Mars Marauders team): Use the tee to connect the pump to two switches. Pumping will send air to both pistons, but one piston is already at the end of its movement and will not move. Or you can move the switch to the middle position for the piston that you don't want to move.
Air tank. Some teams have used the Lego air tank to reduce the amount of pumping that they need to do. The air tank should be connected between the pump and the switches. (Try putting the tank after the switches and see what happens!)

Top: K&S Sta-Flex fuel line, 0.065" inside diameter, part number 410 ($0.29 per foot at Hobbytown in Boise)
Middle: Dubro small silicone fuel line tubing, 1/16" inside diameter, part number 196 ($0.89 per foot at Hobbytown in Boise)
Bottom: Lego pneumatic tubing.
The K&S and Dubro tubing are available from most good hobby shops or on the Internet.
The Dubro silicone tubing has the smallest inside diameter and is easier to use than the K&S tubing because it is more flexible.

Good wheels can be found as part of lego vehicle sets from any department store. You'll have to estimate their cost, but usually it will be about $1 each. The wheels marked "LEGO Group 43.2 x 28 S" on the side wall are popular with rover teams.
Recommended wheels from the Lego web site are listed below. The Red Rover wheels are popular with rover teams and are good wheels.

Most parts are in the "Robotics" section on the left, but it is easier to find items using the Search field.
Large Lawn Tire & Hub (W970111)
Pneumatic Hand Pump (W970117)
Gear Blocks (W970646)
24-Tooth Gears (W970625)
Technic angle beams (W991403)
Chain Links (W970645)
Red Rover Tires and Hubs (W970021) They don't appear to be available anymore.

Lego parts don't work well when forces are trying to pull them apart. There are ways to tie layers of Legos together with other Legos, but it is much easier to use non-Lego parts to do this. Wire and string are much lighter and stronger solutions and should be considered wherever you find Lego bricks pulling apart. Avoid tape, though, because it leaves a sticky residue on the Legos.

If you need to create a platform or container, consider using plastic, cardboard, or fabric instead of Lego parts. They are usually much lighter and make nice rock collecting containers and scoops.

Springs or rubber bands can help offset the weight of a grab arm or scoop. This reduces the load on a piston or motor and can make the arm or scoop quicker and easier to control. (To do: add a diagram or photo)