Who wrote the sonnet beginning 'Shall I compare thee to a summer's day'?

Shakespeare - Sonnet 18, and the joke of it is that the poem answers its own question with no. A summer's day is too short, too hot, too windy and too temporary, and the comparison is rejected in favour of the claim that the poem itself will outlast everything, which it has.

The awkward fact about the sequence is who it is addressed to. The first 126 sonnets are written to a young man, in language that is unmistakably love poetry, and the later ones to a woman described in terms that are frequently unflattering. Editors from the eighteenth century onward went to some lengths about this - one printed an edition changing the pronouns.

The 1609 quarto also carries a dedication to a Mr W.H., described as the only begetter of the sonnets, and nobody has established who that is. Candidates have included Henry Wriothesley with his initials reversed, William Herbert, and a printer's error. The sonnets were published apparently without Shakespeare's involvement, and there is no evidence he ever intended them to be read as a sequence at all.