There is a lot of equipment that a team needs that can be shared by the van.  If you are a team that competes yearly, build two van boxes and store them during the year.  When it is relay time again, you can do a quick inventory, purchase what you need, and be on your way.  Here is a list of supplies for each van box (click here for a printable list):

Cooler with ice
Water
Flashlights
Headlamp, waistlamp or flashlight
Cellphones and/or two-way radios – cell service is spotty in many places on the course.
Clipboard
Timing worksheet, stopwatch or timing software

For more about keeping track of time, check out this article. There are several ways you can keep track of your runners.

Copy of legbook
Runner on road sign
Reflective vests (2 – 3)
Antibacterial soap
Extra garbage bags
Fix a flat
Space blanket
Tea tree oil (or similar) for repellent
DEET repellent
Vaseline
BodyGlide
Icy Hot
Excedrin
Ibuprofen
Benadryl
Sunscreen
Extra batteries
Thermometer (for gauging heat exhaustion)
First aid kit
Blister care kit (Moleskin, secondskin, bandaids)
Wound / sprain care kit (gloves, tape, bandaids, antiseptic wipes, prewrap)
Toilet paper
Scissors
Pens
Reflective tape
Masking tape
Spray bottles

The afternoon legs can be quite warm.  Spray bottles are great to cool off your runner, and most other runners welcome a mist as well. You just might be their hero is you do (but be sure to ask!).  Some teams even bring squirt guns.  You can also purchase a new sprayer like you would use for spraying pesticides and fill it with water for the ultimate sprayer!

Paper towels
Plastic eating utensils
Babywipes
Pepper spray

If you are worried about cougars, pepper spray is the best defense. While chances are really low you would encounter one, the mental relief of having protection can be worth a lot.

Flares
Garbage bags
Window markers

You can find the window markers in Fred Meyer in the school supply section. The ones with the rounded top show up better on tinted windows.