Tim,
About the biggest strategy I have seen lately occurs in those Scramble tourneys, where the team buys mulligans and only uses them for putts. If you need to use a scramble mully for anything but, you really have a problem, and can call home to say you aren't going to win the tournament.
Actually, Jeff, I have been playing some scrambles lately with a couple of guys who play more scramble golf than real golf, and they've proven to me that using mulligans on putts is a waste of money.
They use them on short iron shots, usually wedges.
Think about it.
99% of the teams I see use them on putts of at least 20 feet, which have no more than a 5% chance of going in. Using a Mullie only gives you one more attempt at low odds.
Unless you're all hopeless iron players, it's a better bet that you can improve on 20 feet with your fifth wedge shot, giving you four tries at higher odds.
Playing with them, I have seen the strategy pay off many times.
K