On the way to Whiterun from Riverwood, I rescued a Stormcloak prisoner from some Imperial guards. The Stormcloak guy didn't even say much of a thanks (although I did choose the option to free him). Will freeing prisoners like this affect my standing in the game at all or is it pointless behaviour?
To add immersion to the game, Bethesda added a bunch of "world encounters" that do nothing other than to provide some flavor as you travel around.
Among a ton of other things, Imperials escorting a Stormcloak around the map is one of these random world encounters. You can ignore them or help the Stormcloak: it doesn't matter.
There's another chance to help a prisoner outside of finding a chance encounter on the world map: