It varies hugely from locale to locale on what is acceptable for minimizing trail damage. It really depends on soil type, percentage of clay, how much precipitation you get, how fast it drains and so on. Your local trails group will have information for you. In some areas it's a really big deal, so much as to posted closures. Soils that are high in clay can be some of the worst as they hold ruts for weeks.

In some places, one of the things that happens is that the single track is widened by everyone going around puddles. You get a trail that was 16" wide turning into a much wider path, and not so "single". In other places ruts will hold there shape and deform the trail. Sandy soils drain really fast and is generally not a problem. Like I said, check with your local trails group to see what is recommended for your area.

The city of Boise has a very active trail closure program, for example.
http://www.ridgetorivers.org/etiquette/muddy-trails/