Grammar Girl has an amazing article describing the history, use, and suggestions regarding contractions: “Use contractions in formal writing if it will sound stranger to avoid them than to use them.”
The Chicago Manual of Style says, “Most types of writing benefit from the use of contractions. If used thoughtfully, contractions in prose sound natural and relaxed and make reading more enjoyable.”
Do you remember the character Data from Star Trek? He could not use any form of contraction. Ever. And it set him apart as a non-human. Don’t do that to your writing. Make sure your reader knows there is a human behind the words. Don’t overdo it. There ain’t no reason to sound uneducated in your struggle of pen and paper.