Well, my tastes are idiosyncratic, and I wouldn't particularly recommend them to all and sundry. For what it's worth, the playwright whose feet I tend to worship at is the German Romantic Georg Buchner, who is best known over here for 'Woyzeck', but who wrote two other plays, 'Danton's Death' (a pseuso Shakespearian account of one of the great men of the French Revolution) and 'Leonce and Leyna' (a light comedy about a pair of ill - matched lovers which is just, frankly, odder than that description makes it sound). I love all these plays, mainly because Buchner was capable of expressing in minimal amounts of words the most striking poetic imagery. Ironically, he wasn't even a full - time playwright (he was a biologist who wrote plays on the side) and he died at the age of 23.
I also love a fair bit of that most absurdist of the absurdists, Eugene Ionesco, who wrote a whole series of plays that are sort of funny and sort of disturbing, which is what I tend to approve of in a play (though I do think he had a bit of a tendency to hammer the same points home over and over again).
What is more interesting is the idea that some of the classics are being revisited in this thread. I think everyone tends to assume that just because something is placed on a pedestal, it must have an overinflated reputation - not at all, the reason something becomes 'classic' is because it was good in the first place.
Shakespeare is the man, and provided you can get your head round the language, I think he wrote enough plays to provide something for everyone. The great works are held in the esteem they are for a reason, but all of Shakespeare combines a poetic brilliancy with a tremendously truthful set of insights into human nature and some cracking good storylines (there are even some decent jokes). Not every interesting play is very well known - the Henry VI Trilogy is a fascinating examination of power and corruption, for example, and Timon of Athens is, frankly, almost like a proto -piece of Samuel Beckett. So Shakespeare can always surprise you.
Chekhov deserves the praise heaped upon his plots - Uncle Vanya, in particular, is stunning and devasting at the same time, as is Three Sisters. George Bernard Shaw is actually far, far funnier than I think anyone who hasn't read him would expect. And so on. There is, in other words, always something to be gained from reading the classics - or, indeed, any playwright who has a reputation. Their writing will warrant that reputation.
Personally, for instance, I have no liking for Sarah Kane's work, which I tend to think was needlessly excessive for the sake of it. If it was being staged, I wouldn't rush to see it. But I don't argue with the quality of her *writing*, which I think is evocative and mesmerising, and any actor could learn from reciting.