Typically, the three chords used are the chords on degrees I, IV and V of the scale: in the key of C, these would be the C, F and G chords. Sometimes the V7 chord is used instead of V, for greater tension.
Three-chord songs are easy for the listener to remember, which can make them effective in pop music. They are also easier to learn than other, more complicated songs. Among others, Hank Williams and Bob Dylan have written large numbers of such songs. Punk music very often features three-chord songs - sometimes called a 'three chord thrash' (cf. The Ramones).
"Barbara Ann" by the Beach Boys is a nice example of an effective three-chord song.
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