Now when I say "varnish," I do not mean polyurethane. Varnish as a finish is really quite old, being used in the Orient centuries ago. Varnish is an oil-based finish, usually amber in color. It's sold mostly in quarts and gallons. Adherents claim varnish is the best finish around, better than lacquer or Polyurethane for clear finishes. It's certainly more durable than lacquer, and a special formulation is often used to finish bar tops and other areas where moisture and excessive wear are a consideration. Spar varnish is made especially for outdoor use, deriving its name from its original use in coating the spars on sailing ships.
Varnish dries much more slowly than lacquer, which is both good and bad. It's good in that the slower drying time allows the finish to "flow" longer and remove careless brush marks; bad in that as long as it's wet, dust can settle on a finish and stick to it. This is the primary reason varnish is not used in manufactured furniture. It takes too long to dry. Oil base paint is similar to varnish; it's just got a pigment added to make it opaque.
Since varnish is a more durable than lacquer and was in use before polyurethane was invented, it tends to be favored by many old-timers, if for no other reason than it works ("If it ain't broke, don't fix it!"). It can be a challenge to the novice, however, to get a really smooth finish on a table top. Most people tend to over brush, leaving brush marks in the finish that won't settle out. Others complain of bubbles in the finish. Like James Bonds martini, varnish should be stirred, not shaken. Shaking introduces bubbles into the varnish which take hours, if not days, to settle out. These bubbles will be picked up by your brush and transferred to the piece you're finishing, with disastrous results.
One plus for varnish is that it is it's own sealer; the first coat on a piece after staining can be varnish, either full strength or thinned with paint thinner. If you prefer a more traditional method, you can use shellac as a sealer. Most finishers I know who use varnish as a top coat prefer shellac as a sealer simply because it dries faster, in addition to being easier to sand.
The technique for applying a good varnish finish takes more time to explain than we have space available, but it isn't difficult to learn. Patience, practice, and the proper technique can have you turning out pieces with a truly durable finish in no time. Of course, you'll need a proper brush. I prefer china bristle, which while relatively expensive, is worth the investment. Some finishers I know use a badger hair brush (the ends aren't flagged like bristle brushes), but those are horrendously expensive for the do-it-your-selfer, running $50 and up, each.
For the beginner with varnish, I would suggest thinning the product slightly before you use it. This has two advantages: the finish will dry faster, giving dust less time to stick to it, and it will "lay out" more smoothly, eliminating brush marks. The basic application technique is to lay the varnish on with the grain, then using just the tip of the brush, smooth it out running across the grain. Too much brushing is worse than too little; you'll leave brush marks that won't settle out. Work on about 1 square foot at a time, overlapping the work areas as you go. Needless to say, you want to be in as clean an area (dust free) as possible, with good ventilation and good light. For high use (abuse) areas, varnish is a good durable clear finish, given the time it takes to apply.
If you feel like cheating and don't really want to invest in a good brush anyway, use a foam "throw-away" brush to apply varnish. The construction of the brush won't let you over brush - eliminating the brush marks that more traditional methods leave behind.