Musicologists commonly classify instruments into various categories using Sachs-Hornbostel Classification, a system developed in 1914. It catalogues instruments based on their method of sound production, resulting in five main groups.
Ideophones are instruments that produce sound by vibrating the body of the instrument itself. Examples include clapsticks, cymbals, gongs, bells, mallet percussion, and lamellophones (like the kalimba.)
Membranophones are instruments that have some kind of vibrating membrane; this includes most types of drum, as well as the kazoo.
Chordophones produce sound with a string, usually by plucking or bowing. Examples include zithers, lutes (including modern orchestral strings), and harps.
Aerophones make sound when air is blown through them. The three basic types of aerophone are flutes, reed instruments, and trumpets.
Finally, Electrophones, more properly called radioelectric instruments, produce sound digitally.
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