Here are some musicals on Youtube that I enjoyed:
Next to Normal (This is a brilliant musical. Extremely touching score, and you can't beat Alice Ripley and Aaron Tveit).
Bonnie and Clyde (with Jeremy Jordan and Laura Osnes.. I didn't enjoy the score as much, but the set and costumes are great).
Legally Blonde (super fun musical - starring Laura Bell Bundy and Christian Borle).
Shrek the Musical (I HATE the actual Shrek films, but Sutton Foster is BRILLIANT in this stage adaptation)
Musicals that I love on actual DVD:
RENT
Singin in the Rain (if you want to go old school)
Annie (either the TV version or the original)
Candide (Haven't seen this yet, but I listen to Glitter and Be Gay by Kristin Chenoweth nonstop… also features Patti LuPone… more operatic).
Into the Woods (if you're utterly obsessed with Sondheim like I am… Available on Netflix)
Sunday in the Park with George (this is my favorite musical of all times).
Company (NOT the one on Netflix, that one is SO boring. Try and find the 2012 version with Neil Patrick Harris as Bobby and Patti LuPone. LuPone's "The Ladies Who Lunch" is worth watching the entire show).
West Side Story (always a sucker for this movie… on Netflix now)
Hairspray is always a cute one to go back and watch.
Chicago (I actually liked the movie better than the Broadway production)
If you go on Youtube and just type in "full length musicals" you will get a ton.
Here are some movies that have been turned into musicals that I ADORE. They aren't musicals themselves, but it's pretty cool to watch them and then listen to the cast recordings of the musicals:
Kinky Boots (the movie is beautiful, the show is BEAUTIFUL. If you ever get a chance to see it in NYC, DO.)
Billy Elliot (both the musical movie and the original movie are really great)
Beaches (The regional theatre by my house is turning this into a musical. It's a GREAT movie featuring Bette Midler)
Crimes of the Heart (on Netflix. Not a musical, but it's actually a play. The story is GREAT and if they are ever putting on a regional production of it by you, I highly recommend seeing it).
Big Fish (the cast recording just came out yesterday. I LOVE the movie, and I saw the musical on Broadway twice. The cast recording is NOT to be missed).
I have to say, I'm a very emotional person, so I always lean towards musicals that have a super deep meaning to them. Hence the reason I'm obsessed with Sondheim. I hope this helps, at least a little bit!