Not all of these movies are with the "day-glo nuttiness", but they're huge as musicals. I've listed movies here that not only have wonderful music, but are not the usual run-around-tree songs. Music & dance play an important part in the structure of these films.
1.
Navrang:
V Shantaram's classic, which set the standard for Muscials to come. Very colorful, and a movie that maskes the best use of a classical dancer (
Sandhya, teh director's wife) to the fullest. 50 years since its release, and we can't top it yet.
2.
Teesri Manzil:
Hitchcockian thriller with elaborate Song & Dance sequence (the main lead is a drummer). Has the timeless "Aaja, a-a-aaja" among others.
3.
Padosan: One of the best comedies in India ever, and has the funniest song-scene ever, "Ek Chatur Naar". Also the timeless "Meri Saamne Wali Khidki". Interestingly, both these songs spoof playback singing too.
4.
Guide: About an aspiring (and eventually successful) dancer, who elopes with a tour-guide to fulfill her passion for dancing.
Vijay Anand at the height of his craft to make one of the most wonderful "musical" bollywood movies ever.
5.
Hum Kisi Se Kam Nahi: Arguably one of the biggest musicals of India ever. Includes a 4 (or 5) song song&dance competition that could only have been done with
R D Burman's genuis.
6.
Karz:
Rishi Kapoor does a
Mithun in this movie with Disco being the trend of the time. Reincarnation, classic villain (Sir Juda!) and the most memorable femme fatale of Bollywood. Prime reasons for lots of good music!
7.
Ram Lakhan:
Anil Kapoor (of
Slumdog Millionaire fame) leads the way in this multi-starcast movie with songs for every season: Family, masti and the grand finale at the Thakur's palace.
8.
1942: A Love Story: Epical, but very Musical. Beautiful and elaborate song sequences.
9.
Hum Aapke Hain Koun...!: the modern musical. Two weddings and a Funeral are wrapped around 14 songs! Staged songs, song scenes, dream sequence songs, melodrama songs - it's all there!