Hello all, this is my first post on your sight. I'm going to dive right in with my two cents. LLL is a wonderful and moving play. There are some very silly bits but please take a look at Berowne's "Have at you then, affections men at arms..." speech. It's a wonderful example of rhetoric. Also, Holofernes and Don Armado are very good character parts. My candidates for underappreciated would be the so called romances: Winter's Tale and Cymbeline. Written towards the end of his life, these plays delve into themes of forgiveness and faith and have some beautiful language. From a playwright at the peak of his form.
I second The Winter's Tale. If nothing more, it was certainly Shakespeare's most experimental play, pushing the limitations of the theatre in a way that reminds me of The Beatles in the late 1960s, breaking down the conventions of popular music once they'd mastered it and grown tired of the same old same old. The Winter's Tale also includes one of Shakespeare's best stage directions of all time: "exit, persued by a bear". The only rival to that being the description of Lavenia's entrance in Titus Andronicus.
"Sometimes a thousand twangling instruments will hum about mine ears; and sometimes voices, that, if I then had wak'd after long sleep, will make me sleep again; and then, in dreaming, the clouds methought would open and show riches ready to drop upon me, that, when I wak'd, I cried to dream again"