Avoiding Stupid Mistakes

Don't you HATE it when you solve a problem correctly until the last step...only to be foiled by a careless error? We all know how frustrating "stupid mistakes" can be. Fortunately, there are ways to minimize their occurrence.

Use your scratch paper liberally. Write down all your numbers. If you try to do too much arithmetic, etc. in your brain, it's easy to get mixed up and make a stupid mistake.
Write legibly in your scratch work. This helps prevent those 3s that mysteriously morph into 5s halfway down the page.
As you're doing the problem, think about extreme cases or special cases, such as 0 and negative numbers. In a counting problem, have you counted 0 where it shouldn't be counted? Have you forgotten to count 0 where it should be counted? In a geometry problem that generalizes about different triangles, does the generalization still hold for equilateral triangles? What if one side of the triangle gets reeeeeally big or reeeeally small?
Before writing down your answer, re-read the main question of the problem. Check that you're giving the right information with the right units. If the main question says "How many inches...?" but you wrote your answer in feet, that's bad. If the main question says "What is the y-coordinate of...?" but you only found the x-coordinate...that's bad. If the main question says "What is the volume of the cube?" but you're about to write down the side length...that's bad. Get the point? Don't be bad.
Mentally check whether your answer makes sense. If you're writing down -6 as Bobby's age, then you did something wrong.
On The Big Day, be alert and focused.
PRACTICE! As you do more problems, your stupid-mistake frequency will get lower. During practice, you can also figure out which stupid mistakes you make most often, so that you can take pains to avoid them.