Everyone speaks english because it is a useful, flexible, ever-changing language that is easy to pick up but hard to master.
In Star Trek most aliens don't speak English. The Federation uses unversal translators to translate alien languages.
They speak English because the audience (at least the American audience) speaks English. English, as a West Germanic language, is good for adapting scientific and techonological terms, but then so is modern German. In-universe, there is probably an "official" Federation language, perhaps contrived, such as Esperanto ProfessorTrek 08:11, August 8, 2011 (UTC)