I've seen this topic discussed many ways, from stream crossing to rains, and I think one thing missing is the extent to which your feet will be exposed to wet versus dry conditions. Out west, you may have a short stream crossing followed by the rest of the day in sunny, dry weather. Out east, you may get three days of soaking rain, and have to walk through wet grass and foliage. In the first case, your boots will dry out. In the second case, good luck.
If you're talking about a bit of rain or water, lean toward a synthetic shoe that won't hold much water and will dry quickly. If it's going to be prolonged exposure to water, then either an aquatic shoe, some kind of GoreTex liner, or an overshoe to protect your boot when necessary.
I hike out east mostly, and have to deal with rain and stream crossings, so I picked up a pair of Neos overboots that are almost knee high. Also good for the occasional trek through high mountain snow fields in the spring.