Are there any examples where Judicial Review has not been the process used to deem an act unconstitutional?
The Apportionment Act of 1792 allocating members of the House of Representatives is an example. After it was passed by Congress, President Washington determined that it violated the Constitution in two ways: it gave different states different ratios of population to members of the House, and it gave eight states more than one member of Congress per thirty thousand residents (the Constitution says "the number of Representatives shall not exceed one for every thirty thousand," which can be read as either a restriction on the number of representatives in each state or as a restriction on the total number of representatives). In response, Washington vetoed the bill, and the veto was not overridden (Congress passed a different act, which he signed).
Granted, this never entered into law. However, it was passed by Congress, and preventing the enactment of unconstitutional statutes was one of the original purposes of the veto. If an act isn't deemed unconstitutional through judicial review, it means it was deemed unconstitutional through the political branches of government, by people who are just as sworn to uphold the Constitution as a judge is.