Prune trees for their own health--and for reasons of your own.  You might want to prune:

to remove diseased, dead, or broken branches;
to shape for special purposes--as a shaped specimen or to screen an eyesore, for example;
to renew old plants;
to eliminate suckers and wild growth;
to hold the tree within bounds;
to produce new fall growth for winter color;
to ensure production of larger flowers or fruits;
to aid in transplanting--by compensating root loss.

Keep a few principles in mind.  For example, heavy pruning on top causes leaves and branches to grow.  Heavy pruning of the roots lessens vegetative growth (leaves), but increases production of flowers and fruit.  Heading-back--or cutting back tips--of new growth forces development of lateral branching.

If two branches rub, remove the smaller of the two.  A tree should have only one main trunk.  A secondary leader is no problem when the tree is small.  However, after branches grow larger and heavier, the V-shaped crotch weakens and the tree may split in high winds or snowstorms.  Even a small split offers easy entry for insects.

Remember, the position of branches does not change as the tree matures--a branch that is now a few feet off the ground will always be at about the same height.  It won't rise much higher.  Low branches on mature trees shade the grass and make mowing difficult.

Probably the main pruning principle concerns your own life and limbs: think about what you can do and what you should leave to professionals with heavy-duty equipment.  Large tree limbs and high branches are best left to a professional tree service or arborist.  Also, fill small hollows and squirrel holes yourself, but filling larger ones, especially those marked with fungi, will require the help of a professional tree specialist.

An ounce of prevention
Think ahead.  Taking action now may keep a branch--or the whole tree--from falling on a roof, power line, car--or people.  A good many trees may give warnings for years before disaster occurs.  Check them (especially those friendly old favorite trees) for large open wounds, holes caused by insects and bird nests, disease, fungi, dead tops, and patches of dead bark.  Look for injured roots.  Has there been any excavating near the tree, or has the grade level around it been changed?  Nearby construction in the past 15 years can result in tree root damage long after the building is completed.