Not only poets; lots of famous people have died at age 37, especially scientific and artistic types. (One supposes that if they were not scientific and/or artistic, they probably wouldn't have ended up being well-known.)
Other luminaries who died at age 37: Van Gogh, Majakovskij (who?), Bizet, Burns (the writer?), Hertz.
Contributed by The East Coast 37 Group. Dead poets also mentioned by alert reader bkoz@mit.edu.