Countermeasures to "analysis paralysis"?
Gentle prodding is probably the best suggestion, but if that doesn't do the trick sit them down after the game and let them know what they're doing. A player that over analyzes every move generally isn't much fun to play with, and telling them that (nicely) can help.

If that doesn't work, try practicing with some simple games (for example poker). Once they get used to making faster decisions, it often translates into other games, especially when combined with gentle prodding.

As a final resort, try playing timed games, where the impulse to think long and hard about a decision is countered by a running clock. Good examples are chess/go with a timer, outburst, trivial pursuit, and cranium.