Does anyone know how to get rid of spider mites??

Question:They are on a palm at work I don't want to kill it though!

Answers:
Spider Mites thrive in a dry atmosphere, so "retaining humidity and moisture is a good way to get rid of spider mites." (1) The accumulation of dust on plants also encourages spider mites, so washing off your plants with a heavy spray of water & misting them will help. Use a humidifier & shade plants from direct afternoon sunlight.

Alcohol, oils, and soaps will either suffocate or dessicate the mites.
Some people use a 1:3 mixture of rubbing alcohol to water, mixture, to get rid of Red Spider mites.

Also try this solution:
1/3 cup of rubbing alcohol (80% or more)
1/2 tsp of a mild liquid dish soap
put in a 25-32 oz spray bottle
Fill with water, shake well.

Or
Murphy's Oil Soap spray:
1/3 cup Murphy's Oil Soap
1 tablespoon baking soda
1 gallon water.

There are also Horticultural oils & Insecticidal soaps to kill mites. "Derived from organic soaps like Castile soap, insecticidal soaps kill mites and other plant pests by compromising their cellular integrity, causing cells to rupture and die. The usual recipe is about 2-3 drops of castile soap for every quart of water." (1)

The gardenweb.com site debates Old Spider Mite Remedies such as the home-made rubbing alcohol/soap/water mix ... Murphy's Oil Soap spray... and...even a buttermilk solution. (2)
It works for them! They also discuss Safers insecticidal soap, & Neem oil.

If all else fails the most common miticides are Avid, Kelthane, and just about anything that contains pyrethoids.

Hope this helps!