Those new to Bollywood: you can always SKIP A SONG if you don't like it; I get annoyed by them at times but sometimes they are worthwhile (and the songs are not as often as they used to be nor as long).
This list of movies is great for those who are new to Bolly! Every movie has English subtitles ofcourse.
Update March 11, 2019: 5 fairly recent movies to see
Sanam Teri Kasam
Padmaavat
Raabta
Ghanchakkar
Half Girlfriend
Neerja
Tere Naam
Mr & Mrs Iyer
Manorama 6 Feet Under
Awarapan
Kurbaan 2009
Tum Mile
Meri Brother Ki Dulhan
Barfi
Delhi Belly
Raqeeb
Dhol
Salaam Namaste
Bachna Ae Haseeno
Ijaazat
Jodha Akbar
Hum Dil De Chuke Sanam
Lakshya
Bhool Bhulaiyaa
Page 3
Meri Yaar Ki Shaadi Hai
Love Aaj Kal
Kabhi Alvida Naa Kehna
Life in a Metro
I Hate Luv Stories
Race 1
Race 2
Honeymoon Travels Pvt. Ltd
Heroine (2012)
Hum Tum
Saheb Biwi Aur Gangster 1 & 2
Fanaa
Once Upon a Time in
Mumbai Dobara
Ek Villain
English Vinglish
Life in a Metro
Shootout at Wadala (based on real story)
Dirty Picture (based on real story, Silk Smitha)
Kahaani
Talaash
Udaan
Awarapan
88 Antop Hill
Guzaarish
Hum Tum
Raqeeb
Zindegi Na Milegi Dobora
Go Goa Gone
'
House Full
Race 1
'
Race 2
Shuddh Desi Romance
Rhanjaana
Lootera
Udaan
PK
Table No. 21
Highway
Shankar's I (as in i )
Drishyam
Here are some fantastic Tamil movies - classics and new movies you can see on Einthusan, a great (and legal) website that shows with subtitles. If you pay towards it, you won't see ads! Amazon also has most of these titles.
Subramaniapuram
Raam
Bahubali (Telugu)
Naan Kadavul
Paruthiveeran