In my city (Lansing, Michigan), and apparently in many other cities, you are not allowed trial by jury for traffic violations. This seems to be in direct contradiction to the 7th amendment. Is there a reason for this? Is it unconstitutional?
The Seventh Amendment's jury trial provision does not apply to the states. The Bill of Rights does not inherently restrain the states at all, merely the federal government. The Fourteenth Amendment does restrain the states; notably, it forbids a state from depriving any person of life, liberty, or property without due process of law. Courts have read into "of law" the added requirement that the law be compatible with the fundamental rights that are implicit in the concept of ordered liberty; this means that most stuff that would violate the Bill of Rights if done by the feds violates due process if done by the states. However, not all provisions of the Bill of Rights have been incorporated (i.e. applied to the states); the requirement for a jury in a civil trial is one of the few that hasn't been incorporated, because courts do not consider it a fundamental right (merely one protected in the federal courts).
Now, many traffic tickets are actually misdemeanor offenses, and a jury-trial requirement for crimes is incorporated. However, even for federal offenses, the courts have generally found that the Constitution doesn't require jury trial for petty crimes (those with a maximum sentence under 6 months).
This is the text of the Seventh Amendment:
In Suits at common law, where the value in controversy shall exceed twenty dollars, the right of trial by jury shall be preserved, and no fact tried by a jury, shall be otherwise re-examined in any Court of the United States, than according to the rules of the common law.
"Suits at common law" means (for our purposes) "lawsuits." In other words, the Seventh Amendment applies to civil cases. Traffic tickets are criminal cases, so the Seventh Amendment does not apply to them at all.