I grew up with Jesus Christ Superstar and still love it. Quite possibly my favourite version of the story, together with Last Temptation of Christ, and it's probably got some of Andrew Lloyd Webber's best tunes and Tim Rice's smartest lines. Fiddler on the Roof is also great - with those two, Norman Jewison definitely knew how to translate stage shows onto film. Another musical I loved as a kid and still do: Hair.
More recently, I completely fell for Sondheim's Assassins, a show that's smart and utterly relevant in this day and age. Not sure if the songs themselves hold up all that well for people who prefer more melodious musicals, though. And last year we saw Gypsy in London, with Imelda Staunton. It's a surprisingly subversive, dark musical, though it helps if you watch it without knowing anything about it. At first it seems your usual Technicolor mid-century musical, but it turns out to be considerably more complex than that, and the format of the musical fits it perfectly. The film is also pretty good and has at least one pivotal scene that was actually more effective than in the stage version I saw, but it also tones down the more risky elements a bit.
They're perhaps not technically musicals, but I can absolutely recommend John Carney's Once and Sing Street - and of course the granddaddy of Irish musical movies, The Commitments.