Wax
A very soft "finish" with minimal protective qualities. Best used as a polishing and preserving agent on top of other finishes or as a minimalist finish to preserve the natural color of wood.
Linseed Oil
A natural oil finish made from seeds of the flax plant. One of the least protective finishes but it is easy to apply and yields a beautiful hand-rubbed look. Like all oil finishes, it's best for items that are not subject to a lot of wear and tear.
Tung Oil
An ancient, natural finish made from nuts of the Tung tree. Slightly more water resistant and paler in color than linseed oil. Often used as the base oil component in other finishes. A good choice if you want the hand-rubbed look.
Oil-Varnish Blend
A very popular "hybrid" finish made by mixing a little varnish with a larger quantity of oil. Easy to apply like true oil finishes but with some of the protective qualities of varnish. Group includes antique oil, teak oil, Watco Danish oil, Nordic oil, Scandinavian oil, and various salad bowl finishes.
Shellac
One of the oldest and most under-appreciated of all finishes. More water and scratch-resistant than oil or oil/varnish-blends but not as protective as varnish or water-based finishes. Also dissolves in alcohol so not the best choice for bar tops. Comes in a variety of colors ranging from nearly transparent to orange/amber and is available in flakes or pre-mixed. Easily repaired and not as toxic as oil-based finishes.
Lacquer
Synthetic cellulose-based finish that is the finish of choice for many professionals. It dries fast, has decent protective qualities (somewhere between oil-varnish blends and varnish), provides excellent clarity and depth, rubs out well, and is fairly easy to repair. It also sprays very easily with great leveling properties. Available in several varieties including nitrocellulose (standard), and catalyzed lacquer (is available with the catalyst added). *see "Conversion" for post catalyzed finishes not used by the average woodworker.
Varnish
A very protective and durable amber-colored finish that holds up well to wear and tear, water, and solvents. Commonly available in three flavors, depending on the resin used alkyd, phenolic, or polyurethane. Negatives include long curing time, noxious fumes while curing, and poor repairability. Also yellows more over time so not the best choice for light-colored woods.
Water-Based
Good choice if you're looking for a non-yellowing finish that's safer for you and the environment. Decent toughness and scratch resistance but not as resistant to water, heat, and solvents as polyurethane varnish. First coat has tendency to raise grain. Water-based finishes typically cost more than their oil-based counterparts.
Conversion
Fast curing finish with excellent resistance to heat, wear, and solvents. Typically used for institutional furniture. Highly toxic solvent and formaldehyde fumes -- a professional grade spraying environment is essential. Cellulose Acetate Butyrate (CAB - expensive, tougher, and more resistant) falls into this category. Lacquers made from this very expensive resin are completely crystal clear and non-yellowing.