I know it says plays; but, to me, some of the truly worst adaptations of very good stage shows were mostly musicals.
Musical: In order, Nine, The Producers, A Chorus Line. I loved the first two shows and hated the movies. I can't remember a more static movie than The Producers. They should have just taped it live. Nine was just awful, although some of the visuals were at least interesting. I don't think ANYONE could make a good movie of A Chorus Line. It is just too stage bound. Should have just taped it in front of a live audience. The movie of Mame was also terrible, but -- for reasons that I can't explain -- I have always enjoyed parts of it enough to consider it a guilty pleasure. Looking way back, I actually can't think of anything worse than the above. Maybe A Funny Thing Happened on the Way to the Forum and Finian's Rainbow. I can't actually think of any movie musicals from the thirties, forties and fifties that were as bad as the above.
Play: It is probably that they have just dated so badly, but some Neil Simon movies have been colossally awful. I saw both California Suite and Plaza Suite recently and it was painful to watch them; but, at least with these, the material itself sucked. I suspect that they were dated the day they originally opened on Broadway, however. Also, I dare anyone to sit through The Last of the Red Hot Lovers or Star Spangled Girl or Only When I Laugh, and not want to scream. Two worthy Simon plays that were ruined in the transition to film were Brighton Beach Memoirs and Lost in Yonkers. (There were some good Simon adaptations IMO: Biloxi Blues (although it did sort of highlight that the original play was not as good as was declared when it opened); Barefoot in the Park; parts of The Sunshine Boys and The Odd Couple...although they were more substantial than others listed here, they are still very dated IMO. When is the last time that 'it's either very old meat of very new cheese' get a laugh. Also re non-Neil Simon, try getting through Mary Mary, Forty Carats, Any Wednesday, and you will understand why light comedies are no longer produced on Broadway.
Serious plays: I have always felt that the movie version of The Glass Menagerie was terrible, mainly because Gertrude Lawrence was so wrong. I wonder why anyone even thought to hire her. I have never seen a staging of The Madwoman of Chaillot (Dear World doesn't count), so I may be cheating, but that movie was atrociously bad. Agree re The Children's Hour, although I liked Audrey Hepburn. Although James Earl Jones and Jane Alexander both received Oscar nominations (in very weak years), the movie version of The Great White Hope paled in comparison to the play. I am sure there are a lot of others, but these are the ones that come to mind.
PS -- I loved Bus Stop and Arsenic and Old Lace, and thought that Rabbit Hole was very well done, especially the performances of Nicole Kidman and Miles Teller.