Estienne du Tertre published suyttes de bransles in 1557, giving us the first use of the term, although the usual form of the time was as pairs of dances. The first recognizable suite is Peuerl's Newe Padouan, Intrada, Dantz, and Galliarda of 1611, in which the four dances of the title appear repeatedly in ten suites. The Banchetto musicale by Johann Schein (1617) contains 20 sequences of five different dances.
The "classical" suite consisted of allemande, courante, sarabande, and gigue, in that order, and developed during the 17th century in France, the gigue appearing later than the others. Johann Jakob Froberger is usually credited with establishing the classical suite through his compositions in this form, which were widely published and copied.
Many later suites included other movements placed between sarabande and gigue. These optional movements were known as galanteries: common examples are the minuet, gavotte, passepied, and bourree. Often there would be two contrasting galanteries with the same name, e.g. Minuet I and II, to be played alternativement, meaning that the first dance is played again after the second, thus I, II, I.
The later addition of an overture to make up an "overture-suite" was extremely popular with German composers; Telemann claimed to have written over 200, J.S. Bach had his four orchestral suites, and George Frideric Handel put his Water Music and Music for the Royal Fireworks in this form.
Handel wrote 22 keyboard suites, while Bach produced multiple suites for cello, violin, flute, and other instruments, as well as his English suites, French suites and Partitas for keyboard. For Bach especially, the suite form was a base on which to spin more elaborate sequences. Francois Couperin's later suites often dispensed entirely with the standard dances and consisted entirely of character pieces with fanciful names.
By the 1750s, the suite had come to be seen as old-fashioned, superseded by the symphony and concerto, and we see few composers still writing suites. In the 19th century the term made a comeback, but now meaning either an instrumental selection from a larger work such as an opera or ballet, a sequence of smaller pieces tied together by a common theme, such as the nationalistically inflected suites of Grieg, Sibelius, or Tchaikovsky, or a work deliberately referential of Baroque themes, as in the mischievous Suite for Piano by Arnold Schoenberg. Another famous example of an early 20th century suite is The Planets Suite by Gustav Holst, in which a different piece was written to represent each planet in the solar system (except Earth and Pluto).