Disclaimer: Since the question is about the Best dance sequence and not the famous dance sequence, The dance numbers I am going to include are solely based on its quality rather than popularity.
I see some excellent answers here. Most of the recent dance sequences are already covered under different answers.However, the list is incomplete without few famous and not so famous but amazing dance sequences.
The first one on my mind is from movie Kalpana (1960). The classical song- Tu hai mera prem devata is beautiful rendered by legends -Mohd. Rafi and Manna Dey and composed by O.P. Nayyar.
The song is filmed on real life sisters Padmini and Ragini of famous Travancore Sisters. It is my personal favorite and I don't think any other dance in any Bollywood movie can beat it.Please watch it to believe it.
The next one on my list is from Jhanak Jhanak Payal Baje. The film is directed by V. Shantaram and as the name suggests, the movie has dance at the center of the story. It features legend classical dancer Gopi Krishna and a regular face in Shantaram's film- Sandhya who is also a classically trained dancer.
I am posting three dances from the movie. I understand that it might be boring to the people who do not like classical dance but I urge to watch entire video at least one time.
Vyanjanthimala has graced many bollywood films with her beautiful dances. Few of her my most favorite dance numbers apart from Hothon pe aisi baat are
1. Movie: Phoolon ki Sej (1964) also featuring Gopi Krishna
2. Movie: Amrapali (1966)3. Movie: Dr. Vidya (1962)
Some must see Dance offs/ Dance Sequences
Vyanjanthimala Vs. Helen
Very few people may know that there are more than one dance sequence featuring Bollywood's two best dancers.
This one is from movie Dr. Vidya (1962).
Movie: Prince (1969)
Vyanjanthimala Vs. Padmini
Movie: Raj Tilak (1958)
Helen Vs. Ragini
Movie: Shikari (1963)
Other examples of best dance sequences include
Movie: Azaad (1955)There are many more dance numbers that definitely need to be included here.
There is one more movie - Navrang (1959) by V.Shantaram featuring Sandhya which is famous for its choreography and some never seen before dance in Indian cinema. I think someone has posted videos in his/her answer.
I will add other dance sequences later as it is 5:00 a.m. and I should rest.