Ashtakam or Astakam is derived from the Sanskrit word ‘Asta’ which means ‘eight’. Ashtakam is basically a poetic composition consisting of 8 stanzas. Each stanza has 4 lines and so an ashtakam consists of 32 lines. These lines follow a strict rhyme scheme.
Adi Sankaracharya the great Indian philosopher and theologian is one of the best known composer of ashtakams in Sanskrit. He has written more than 30 ashtakams in praise of various Hindu deities.
A list of Astakams in English is available here.