Below is an interesting article I found that I am reposting here. The comments and opinions stated below are from the original author.
Natural Spider Mite MiticideBy Carl L. Rosner
Fill a gallon jug with water and add one (1) or two (2) tablespoons of dishwashing detergent and one (1) tablespoon of vegetable oil (or Neem oil). Shake up the gallon jug to mix the ingredients.
Fill this solution from the gallon bottle into a spray bottle and just before using add 1 to 2 two caps full (from the rubbing alcohol bottle) of rubbing alcohol and spray immediately. If you do not use the full bottle of spray, I suggest the next time you are going to use the soap/alcohol solution add the same amount of rubbing alcohol again, since the alcohol will evaporate. I store this soap/oil solution in the gallon jug for months on end. It does not seem to go bad.
Spray on plants covering all leaf and stem surfaces. You may have to spray from three to four times with intervals of three days. I have eliminated almost any kind of pest that has attacked my trees, including scale.
I do not wash off the spray and have seen no adverse reaction to the trees from this mixture.