They are - Woodwinds, Percussion, Strings, and Brass. These families are based on the physics of how the music is produced ... Woodwinds produce music because of vibration of a reed or wind passing through a narrow passage (flute, bassoon etc), Percussion is due to vibration of a membrane (drums), Strings produce music through vibration by striking or plucking a string, Brass produces music through resonating harmonic chambers. Keyboards are a class of instruments that really fit into one of these classes depending on what the keys do. Piano is really a string instrument, organ is woodwinds etc. And finally, I have excluded all electronic/modern instruments.

[Sorry this is so long -- the topic is interesting.] Arguably there are only three, classified by how one makes the noise: scraping, blowing, hitting. We get four by subdividing blowing, the wind instruments, into woodwinds and brasses, on aesthetic and historical grounds rather than physics. Scraping and blowing both yield not just pitched notes but continuous tones -- the tone can be sustained and can grow louder or softer. Hitting gives only non-continuous tones, which may or may not be pitched, but which all begin to decay, quickly or slowly but inevitably, as soon as they occur. Scraping gives the strings: violins, violas, cellos, basses, and some older members of the family lately being rediscovered, viola da gamba, cello d'amore. The continuous tone stems from an ongoing, very complex stick-slip relationship between the string itself and the rosined bow strings drawn back and forth at various speeds and pressures across it. And then the string can be plucked, making it for a few seconds percussive. Blowing vibrates a column of air somehow. It's a woodwind if we vibrate a reed at the end of that column to get it going (the clarinets, oboe, English horn, bassoons, saxophones, bagpipes, harmonica, various reed organs in the form of large and small accordions, diesel horns) or direct air over an edge that splits the air stream and sets the enclosed part vibrating (flutes, recorders, ocarinas, police, bo's'n and referee whistles, steam whistles, slide whistles, dog whistles). Pipe organs should be in here, but it's hard to picture a large one as a woodwind -- they're more like a species unto themselves. Steam calliopes -- a steam driven pipe organ -- are also wind instruments, but those who have been close to one say they're more like a force of nature. The brasses also vibrate a column of air continuously, but what vibrates is the players' lips, as they blow straight into the end of the bugles, trumpets, trombones, tubas, French horns, tubas, alpenhorns, rams' horns, hunting horns, or dried seaweed, which in appropriate lengths can be played like a bugle with a trumpet mouthpiece. Ditto lengths of garden hose, which is useful for convincing people that the shape of the tube has nothing to do with the timbre or pitch of the instrument. And then there's percussion -- the stuff we hit: drums of all sorts and sizes, cymbals ditto, tam-tam ("gong"), wood blocks, hoof-cloppers, whips, tambourines, castanets, rattles, triangles. And though all percussion instruments share the quality of being non-sustaining, some are nevertheless pitched, giving off definite notes: timpani, bells, xylophone, glockenspiel, vibraphone -- and piano. Yes indeed, it may be full of strings, years, and honors, but there's no doubt that a piano is a percussion instrument, each note caused by an impact and inevitably decaying from that moment. Granted, some composers and players can make us forget the fact. But then some are intent on reminding us. Think the Schuman "Carnaval." Think Jerry Lee Lewis. Which leaves the string instruments that are only plucked, never bowed: various guitars, mandolin, banjo, lute, harpsichord (strings picked by a plectrum, not struck). They don't strike us as percussion, but then neither does a piano, and the fact is they have the essential percussion quality of being non-sustaining. (And note that when a jazz player refers to a "rhythm section," she means piano, bass, drums, and perhaps guitar.) So maybe we just need to expand our instinctive picture of what "percussion" means beyond the remembered rhythm bands of childhood. [Obviously this is only about Western instruments. Include the Orient and you're going to need an encyclopedia. But the categories, scrape, blow, hit, remain an interesting way to begin looking at any instrument.]