@tyro3 - One reason you may not be able to seize a wandering missionary is you may have an active peace treaty with that missionary's civ (10 turns at Standard speed). Seizing a missionary is an act of war, but you can't DOW during an active peace treaty.
@Polisurgist - You certainly can capture Greeat Prophets, and Missionaries. Agree that captured GrPrs and Missionaries are mostly useless. Missionaries can be used as scouts (4 movement points isn't bad), but they will suffer attrition and die in foreign territory without open borders. Great Prophets that still have 4 spread missions left can be used to form a Holy Site or to found or enhance a religion. They shouldn't be used to spread, since they do retain their old religion (so you would be spreading that religion, not yours). They don't suffer attrition, and don't need open borders, but only 2 movement points means they are a tedious way to scout.
Also if you are playing as Sweden, a GrPr that has even 1 spread mission left can be gifted to a CS for 90 influence.