One question I regularly hear from woodworkers asks "How many teeth saw blades should I buy to get the best, smoothest cuts?"
Well, the answer is a little bit more complicated than that, but it doesn't necessarily have to be once you understand how saw teeth work.
Typically, the more teeth a saw blade has, the smoother the cut. It really doesn't matter whether this is the number of teeth overall on a saw blade for your table saw, miter saw or circular saw, or the number of teeth per inch on jigsaw, scroll saw or band saw blades.
Saw blades with fewer teeth will be more aggressive but will produce somewhat rougher finishes. This is because the fewer the number of teeth on the blade, the deeper the gullets in-between the teeth, each of which stores the sawdust until the corresponding tooth clears the blade.
The problem is that with more teeth, the smaller the gullets will be in-between the teeth, which means that the cuts will naturally be slower and less aggressive. There is a fine line to walk here because the slower the cut, the more likely the wood is to be burned as a process of cutting. If there's no place for the sawdust to go, more friction will occur, the blade will be more likely to bind and produce less than desirable results.
As a general rule, I recommend that a woodworker have a few different blades on hand for each tool. For instance, on a 10" table saw, I'd keep a 40-tooth blade for general purposes, an 80-tooth blade for plywood and veneers and a specialty ripping blade for making rip cuts.
On a band saw, I keep a few different thickness blades depending on the sharpness of the curves being cut. For instance, I keep a 1/4" blade for rather tight curves, a 1/2" blade for general band saw cuts and a 3/4" blade for resawing. (If my band saw could accommodate one, I'd keep a 1" blade for resawing, as it would be more stable with less flex.) The 1/2", 3/4" and 1" blades would probably all be 3TPI (teeth per inch), whereas thinner blades would have a greater number of teeth per inch.