Power Tools
Band Saw

Shixart1985, CC BY 2.0, via Wikimedia Commons
A band saw drives a continuous toothed blade in a loop around two or three wheels, feeding a workpiece into the moving blade from below rather than spinning a fixed circular blade the way a table saw does. That continuous-loop design does two jobs almost nothing else does well: resawing thick stock into thinner slices, and cutting curves a straight-bladed saw simply can't follow.
Resaw height is the number that actually matters
Resaw height -- the maximum distance between the table and the upper blade guide -- is effectively the thickest board a band saw can stand on edge and slice through. A saw with 6" of resaw height cannot touch 8" stock no matter how good everything else about it is. See Buying a Band Saw for the fuller breakdown, including wheel size and motor power tradeoffs that follow directly from how much resawing a shop actually plans to do.
Blade width, and the tradeoff it sets
Narrow blades (1/8"-1/4") cut tight curves -- the reason to own a band saw for scrollwork or curved parts at all. Wide blades (1/2"-1") track straighter and resist drift, which is what resawing and straight ripping actually want. Most saws run either, but expect to swap blades between a curve-cutting session and a resawing one rather than owning one blade that does both well.
Setup matters more here than on most machines
Blade tension and tracking affect a band saw's cut quality more than almost any other machine's setup does -- a poorly tensioned or badly tracked blade drifts off a straight line regardless of how capable the saw is on paper. Learning to set drift angle and tension properly, rather than blaming the machine for a wandering cut, is most of what separates a frustrating band saw from a genuinely useful one.
Safety
Keep fingers well back from the blade's front edge during a cut, use a push stick on narrow rip cuts the same as on a table saw, and check blade tension before every session -- a blade that snaps under tension, or that's so loose it wanders off the wheels mid-cut, is a real hazard.
Popular Brands
Images

Product: A band saw's blade guide and tensioning mechanism, mid-cut — Shixart1985, CC BY 2.0, via Wikimedia Commons

