Pan/Tilt head: Head with two or three different planes that are adjusted one at a time usually with the assistance of a separate handle for each plane.
Pros: Easy to adjust in small increments just where you want it, one plane at a time. Sturdy.
Cons: Cumbersome to adjust. You are making adjustments one plane at a time. Head is cumbersome to haul around.
Personal Recommendation: Studio work, product shoots, architectural shoot, fine detail shoots.
Ball Head: A head based on a ball in a socket that supports the body/lens.
Pros: Easy to adjust quickly in all planes at once. Smaller in size. Stable, low center of gravity. Compact, easy to haul around.
Cons: Unless you are willing to pay big money for a top of the line ball head you will usually get a small amount of creep when you lock the ball. Unless you either pay attention or have one with separate friction control it is easy to loosen the ball lock too much and have camera flop unless you are supporting it with the other hand. Ball heads without a separate panning control are hard to use for panorama shots.
Personal Recommendation: Best all around compromise for a field setup. Easier to use and carry for general field work.
Side handle ball head: Ball head with a side handle instead of a knob for ball control
Pros: Easy to adjust quickly and accurately. Stable with general use glass. With add on shutter release it is easy to adjust and shoot without moving your hand away.
Cons: Not as easy to haul around as a standard ball head. Not designed for bigger glass. Usually no separate panning feature.
Personal Recommendation: Excellent in studio for portrait type work.
Panorama Head: Pan heads tend to be based on an L bracket type setup with the ability to raise and lower the body/lens over the head. It also allows the body and lens to be moved forward and backward so the nodal point of the lens is centered over the pivot point of the head.
Pros: Excellent for Panorama shots. Very accurate when set up properly.
Cons: Not much good for anything except Panorama shots. EXPENSIVE.
Personal Recommendation: Panorama photography
Gear Head: A gear head is usually a two plane head that adjusts up and down and side to side on a gear system.
Pros: Very accurate for the limited amount of movement available.
Cons: Limited amount of adjustment, very slow to operate.
Personal Recommendation: Technical photography where accuracy is a must.