Why do some trials not have a jury?

Juries are only required to be an option in matters of law. Matters of equity are generally always in front of a judge except in matters where a case has both law and equity claims. And in those cases, the equity matters will be decided by the judge and the matters at law will be decided by a jury.

Matters of law include any suit for monetary damages ($20 or greater) or criminal matters punishable by more than 6 months in jail (federal law). State laws can differ slightly.

Matters at equity are suits for injunctions, specific performance, and custody and divorce disputes.

And you indicated this was a criminal trial. A defendant can always waive a jury trial if he/she wishes but they generally don't because juries tend to be more favorable to defendants than judges. If a defendant has been accused of a crime that the defendant believes no jury would be able to fairly decide (such as maybe a high profile serial killer) they might consider a bench trial over having a jury that wants to hang him/her before even entering the courtroom.

Depends on the charge.

Most cases that do not involve jail time, like many violations and some misdemeanors in most states do not warrant a jury.

A felony, which can land you in prison for a year or more, are required jury trials by the US Constitution with the exception of those cases where a jury trial is waived by a defendant.

You have a right to request a non-jury trial, otherwise known as a Bench Trial. The advantage to this is that juries typically are biased and go into court the first day already believing that you are guilty. A bench trial is especially beneficial if you are claiming that your civil rights were violated or that there is not enough evidence against you, since the judge is also a lawyer and will make a decision based off of his knowledge of the law instead of his personal thoughts or emotions.

The defendant has the right to wave a trial by jury