The short answer is only the defendant. However, if you are a plaintiff and the defendant filed a counter-claim against you and you lose on that claim, you can appeal. Since the appeal is from the judgment, and a small claims appeal is a trial de novo, it is an appeal of the entire case and both claims will be decided anew. Want proof? See, Code of Civil Procedure Sections 116.710(a),(b) and 116.770(d).