Vatapi Ganapatim Bhajeham --------Muthuswami Dikshitar
From Vinayaka Chavithi (Telugu)
http://www.youtube.com/watch?v=DYvyrtL6hO0
The song starts with a slokam on Ganapati that is not part of the composition 'vatapi.....'.
There was a time when carnatic concerts began with this composition. That has changed now! :)
The raga is Hamsadhwani.
Bruhi Mukundeti Rasane ------- Sadasiva Brahmendrar
From Savitri (Tamil) (1941)
M.S.Subbulakshmi, as Naraadar, sings in Kurinji:
http://www.youtube.com/watch?v=HFOFdQ5xYM0
Jaya Jagadeesa Hare(Pralaya Bayodhi Jale) - Ashtapathi --Jayadeva
From Anandh Math (1952)
Jaya Jagadeesa Hare ...........Kesava Dhrutha Meena Sareera........
http://www.youtube.com/watch?v=zm7hp9K-ing
This is the first Ashtapathi on Dasavataram ( meena sareera to Kalki sareera)
Classical rendition by M.S.Subbulakshmi is available in youtube.
Pahimam Sri Rajarajeswari.........Maha Vaidyanatha Sivan
From Kudumbasametham (1982) (Malayalam)
Pahimam Sri Rajarajeswari Krupakari Sankari............. in Janaranjani
http://www.youtube.com/watch?v=Sh-bDkLMV6Q
Pavana Guru Pavana pura Lalita Dasar
From Mella Thirandhadhu Kadhavu (1986) (Tamil)
Pavana Guru Pavanapura................in Hamsanandhi
http://www.youtube.com/watch?v=s9gs0r7_0J8
I was surprised to see a Sanskrit Classical Composition in a Tamil movie of the 80s ! :) The song is not even included in the list of songs in the movie.
Manikya VeeNaam(Shyamala Dandakam)............................Kalidasa