I’m not in love with musicals, although there are a few that I genuinely like. My roommate detests them! Anything we might enjoy together? We both LOVE, LOVE Across the Universe, for example. Thanks!
CHICAGO is probably the most popular musical movie I know with friends who don’t ordinarily like musicals, with SWEENEY TODD second. (Personally I loved the former, hated the latter.)
The movie CABARET is also popular, I think partly because the musical numbers all take place in a nightclub (i.e. it’s not characters bursting into song in the real world).
South Park: BL&U - Best. Musical. Evar.
Also Hedwig & the Angry Inch.
Dr. Horrible’s Sing-Along Blog - short, web-released musical from Joss Whedon
Once is a different sort of musical. Kind of a “realistic” musical.
What about animated movies? There’s the whole Disney catalog, including the live-action **Enchanted **from a few years ago.
Also, **The Nightmare Before Christmas **is a favorite of mine.
I liked the music in Moulin Rouge, though I didn’t care for the characters and plot.
Great ideas, all! Although the room mate detested Moulin Rouge and Sweeney Todd; both of which I happen to love…go figure!
Little Shop of Horrors
Rocky Horror Picture Show?..no?..well, I usually have it playing on Halloween night while I’m handing out candy at the door.
A Hard Day’s Night? Help!? Yellow Submarine? The King and I?
What is it about musicals that you don’t like? If we knew that, we could do a better job of recommending movies for you.
For many, it’s that they’re “not realistic,” but if you liked Across the Universe, that’s obviously not a problem for you. 
In the 50s, there was a trend on Broadway towards making testosterone-driven musicals that men wouldn’t be embarrassed to see: Guys and Dolls, South Pacific, Damn Yankees, Li’l Abner. Maybe one of these would do the trick?
I’ll suggest Tommy - songs they probably already know but will hear in a different context, just like Across The Universe.
Seconding it. It’s a lot of fun. I don’t like the movie as much as the stage version but it’s still great.
Did you try Rent? I only tried it because Rosario Dawson was in it, but I was hooked by the first song “Seasons of Love” and there are several other good songs in the show.
Jersey Boys
My girlfriend and I liked American Idiot. We also happened to catch it the week Billie Joe Armstrong was performing.
Maybe the OP doesn’t like show tunes? If that’s the case, more pop-band oriented shows might be the way to go.
I don’t what it is about musicals, but I always find myself staring at the Playbill counting down songs until the end.
Hair,* Jesus Christ Superstar * are both good. IMHO the best contemporary musical ever written is Joseph and the Amazing Technicolor Dreamcoat.
Sound of Music is a great intro to classic musicals.
I really don’t like musicals at all, except for All That Jazz, and Fame– the movies, I don’t even know if there are stage versions.
All That Jazz has the advantage of being about a choreographer. so it at least makes sense that the people are frequently bursting into song and dance.
Likewise with Fame, about kids at a performing arts school.
I detest musicals and enjoyed Guys and Dolls.
I can’t believe we totally forgot about…
Grease
I’ve never met anyone who didn’t love that movie. Who doesn’t love Olivia Newton John? 
I’ve also seen the play performed at college.
My Best Friends Wedding is kind of a musical. People sure do sing a lot in it but it is practically a ‘regular’ movie.
Not a ‘musical’ but Strictly Ballroom has plenty of dancing so it is musical-ish and it is one of the funniest movies ever.
Cats is a musical for people who don’t like musicals.
There is no movie version but Sunset Blvd is excellent. How about EVITA?
Speaking of Alan Parker how about the movies The Commitments and The Wall?