For some types of cases, such as those involving child support or custody, or a request for an injunction (to stop the city from cutting down a tree, for example), you are not entitled to a jury, but in most civil cases, including those involving personal injury, breach of contract, professional malpractice, libel, or slander, you are entitled to a jury trial if you want one.
You may, however, want to think twice before you request a jury trial; it will be more complicated and harder to handle a case before a jury on your own than it would be to represent yourself before a judge. It can be tricky, for example, to participate in the jury selection process. Most who go it alone are better off avoiding this added level of complexity by trying their case in front of a judge -- but, of course, the other party has a say, too, and if that person demands a jury, so be it.
Trying to decide whether it's better to have a judge or jury hear your case? Check out Nolo's article Judge or Jury Trial: Which is Better?