Fermi problems: making a quick order-of-magnitude estimate of a quantity based on rough, but guessable quantities. Not only is this immensely fun, it has many practical applications to quickly rule out unrealistic hypotheses. Solving these in real-life situations (they come up surprisingly often) may also impressive others - your mileage may very, of course.

Dimensional Analysis: either checking the units of a possible answer, or guessing a formula based off the only likely possibility that gives the necessary units. Look at Street Fighting Mathematics section "Dimensions" for some great applications.