The most uncommon taal in Hindi film songs is the Jhap Taal of 10 beats. I have already given a more or less exhaustive list of Hindi film songs in Jhap Taal. The second most uncommon taal is Roopak Taal, based on a rhythmic cycle of 7 beats. Some of the songs may be in other taals (Jhumra, Deepchandi, Dhamar, Aadachautaal, etc.) based on the same rhythmic cycle of 7 beats or multiples of 7 (mainly 14).
I present here a more or less exhaustive list of 124 Hindi film songs in Roopak Taal and other Taals of the same rhythmic cycle (of which two songs, from Arzoo and Zindagi Aur Maut, are repeated in the list as male and female versions respectively).
1. Gham Diye Mustaqil- K L Saigal (Shah Jahan- Naushad)
2. Tere Mandir Ka Hoon Deepak- Pankaj Malik (nonfilm)
3. Dhas Na Jaye Tujhko Zulfen- Mohd Rafi (Malika- A R Qureshi)
4. Le Ja Uski Duaen O Jo Tera Ho Na Saka- Mohd Rafi (Heer- Anil Biswas)
5. Ajab Teri Maya- Mohd Rafi (Punarmilan- C Arjun)
6. Mujhe Darde Dil Ka Pata Na Tha- Mohd Rafi (Akashdeep- Chitragupt)
7. Zindagi Bhar Gham Judai Ka Mujhe Tadpayega- Mohd Rafi (Miss Bombay- Hansraj Bahl)
8. Hui Sham Unka Khayal Aa Gaya- Mohd Rafi (Mere Hamdam Mere Dost- Laxmikant Pyarelal)
9. Mujhe Bhool Jana Agar Ho Sake- Mohd Rafi (Taqdeer- Laxmikant Pyarelal)
10. Tujhe Kya Sunaun Main Dilruba- Mohd Rafi (Aakhri Dao- Madanmohan)
11. Apni Azadi Ko Ham Hargiz Bhula Sakte Nahin- Mohd Rafi (Leader- Naushad)
12. Aaj Galiyon Mein Teri- Mohd Rafi (Sohni Mahiwal- Naushad)
13. Teri Mehfil Tera Jalwa- Mohd Rafi (Sohni Mahiwal- Naushad)
14. Subhanallah Haseen Chehra- Mohd Rafi (Kashmir Ki Kali- O P Nayyar)
15. Na Jane Kyon Hamare Dil Ko Tumne- Mohd Rafi (Mohabbat Zindagi Hai- O P Nayyar)
16. Meri Duniya Lut Rahi Thi- Mohd Rafi (Mr and Mrs 55- O P Nayyar)
17. Dil Lege Daga Denge Wo- Mohd Rafi (Naya Daur- O P Nayyar)
18. Raat Bhar Ka Hai Mehmaan Andhera- Mohd Rafi (Sone Ki Chidiya- O P Nayyar)
19. Hai Bahare Baage Duniya Chand Roz- Mohd Rafi (Bambai Ka Chor- Ravi)
20. Haye Re Insaan Ki Majbooriyan- Mohd Rafi (Ghunghat- Ravi)
21. Zara Sun Hasinae Nazneen- Mohd Rafi (Kaun Apna Kaun Paraya- Ravi)
22. Kal Chaman Tha Aaj Ik Sehra Hua- Mohd Rafi (Khandaan- Ravi)
23. Apni To Har Aah Ik Toofan Hai- Mohd Rafi (Kala Bazar- S D Burman)
24. Kahin Bekhayal Ho Kar- Mohd Rafi (Teen Deviyan- S D Burman)
25. Na Kisi Ki Ankh Ka Noor Hoon- Mohd Rafi (Lal Qila- S N Tripathi)
26. Wo Saba Kehna- Mohd Rafi (Kabuliwala- Salil Chowdhury)
27. Nava Kalpana Nava Roopa Se Rachana Rachi- Mohd Rafi (Mrig Trishna- Shambhu Sen)
28. Aji Hamse Bachkar Kahan Jaiyega- Mohd Rafi (Arzoo- Shankar Jaikishan)
29. Keh Do Koi Na Kare Yahan Pyar- Mohd Rafi (Goonj Uthi Shehnai- Vasant Desai)
30. Mujhe Raat Din Ye Khayal Hai- Mukesh (Umar Qaid- Iqbal Qureshi)
31. Khush Raho Har Khushi Hai Tumhare Liye- Mukesh (Suhaag Raat- Kalyanji Anandji)
32. Manjhi Naiya Dhoondhe Kinara- Mukesh (Uphaar- Laxmikant Pyarelal)
33. Hiya Jarat Rahat Din Rain- Mukesh (Godaan- Ravi Shankar)
34. Mujhe Tum Se Kuchh Bhi Na Chahiye- Mukesh (Kanhaiya- Shankar Jaikishan)
35. Lakkhi Babul Mere Kahe Ko Dini Bides- Mukesh (Suhaag Raat- Snehal Bhatkar)
36. Barkha Rani Zara Jamke Barso- Mukesh (Sabak- Usha Khanna)
37. Doli Mein Bithayke Kahar- S D Burman (Amar Prem- R D Burman)
38. Prem Ke Pujari Ham Hain- S D Burman (Prem Pujari- S D Burman)
39. Main Teri Nazar Ka Suroor Hoon- Talat Mehmood (Jahan Ara- Madanmohan)
40. Ye Hawa Ye Raat Ye Chandni- Talat Mehmood (Sangdil- Sajjad)
41. Ae Mere Pyare Watan- Manna Dey (Kabuliwala- Salil Chowdhury)
42. Ud Ja Bhanwar- Manna Dey (Rani Roopmati- S N Tripathi)
43. Dil Laga Kar Ham Ye Samjhe- Mahendra Kapoor (Zindagi Aur Maut- C Ramchandra)
44. Jagat Bhar Ki Roshni Ke Liye- Hemant Kumar (Harishchandra Taramati- Laxmikant Pyarelal)
45. Kho Gaya Jane Kahan Arzuonka Jahan- Hemant Kumar (Mohar- Manna Dey)
46. Chupke Chupke Raat Din- Ghulam Ali (Nikaah- Ravi)
47. Dil Lagakar Ham Ye Samjhe- Asha Bhosle (Zindagi Aur Maut- C Ramchandra)
48. Saba Se Ye Keh Do- Asha Bhosle (Bank Manager- Madanmohan)
49. Ab Ye Bata Jayen Kahan- Asha Bhosle (Baap Re Baap- O P Nayyar)
50. Aaj Koi Pyar Se Dil Ki Baaten Keh Gaya- Asha Bhosle (Sawan Ki Ghata- O P Nayyar)
51. Main Shayad Tumhare Liye Ajnabi Hoon- Asha Bhosle (Ye Raat Phir Na Ayegi- O P Nayyar)
52. Mohabbat Cheez Hai Kya- Asha Bhosle (Ye Raat Phir Na Ayegi- O P Nayyar)
53. Ja Ri Sakhi Saj Dhaj Ke- Asha Bhosle (Ghunghat- Ravi)
54. Ik Pyar Ke Bandhan Ke Khatir (happy version)- Asha Bhosle (Pyar Ka Bandhan- Ravi)
55. Na Jaiyo Re Sautan Ghar Saiyan- Asha Bhosle (Kagaz Ki Nao- Sapan Jagmohan)
56. Ab Ke Baras Bhej Bhaiya Ko Babul- Asha Bhosle (Bandini- S D Burman)
57. Dhalti Jaye Hamari Chundariya Ho Ram- Asha Bhosle (Nau Do Gyarah-S D Burman)
58. Thandi Thandi Sawan Ki Fuhar- Asha Bhosle (Jagte Raho- Salil Chowdhury)
59. Kya Kahen Tujh Se Mohabbat Ho Gayi- Asha Bhosle (Jantar Mantar- Sardar Malik)
60. Geet Kitne Ga Chuki Hoon- Asha Bhosle (nonfilm)
61. Balam Se Milan Hoga- Geeta Dutt (Chaudhvin Ka Chand- Ravi)
62. Banni Teri Bindiya- Lakshmi Shankar (Do Boond Pani- Jaidev)
63. Chali Ban Ke Dulhan- Lata Mangeshkar (Subah Ka Tara- C Ramchandra)
64. Sun Ri Sakhi More Sajna Bulaye- Lata Mangeshkar (Nagin- Hemant Kumar)
65. Ye Neer Kahan Se Barse- Lata Mangeshkar (Prem Parbat- Jaidev)
66. Aaj Dil Pe Koi Zor Chalta Nahin- Lata Mangeshkar (Milan- Laxmikant Pyarelal)
67. Jiya Naahin Laage Ka Karun Sajna- Lata Mangeshkar (Sau Saal Baad- Laxmikant Pyarelal)
68. Bandhan Toote Na Sanwariya- Lata Mangeshkar (Mom Ki Gudiya- laxmikant Pyarelal)
69. Aap Ki Nazron Ne Samjha Pyar Ke Qabil Mujhe- Lata Mangeshkar (Anpadh- Madanmohan)
70. Hai Isi Mein Pyar Ki Abroo- Lata Mangeshkar (Anpadh- Madanmohan)
71. Kabhi Ae Haqeeqate Muntazar- Lata Mangeshkar (Dulhan Ek Raat Ki- Madanmohan)
72. Aaj Socha To Ansoo Bhar Aaye- Lata Mangeshkar (Hanste Zakhm- Madanmohan)
73. Kho Diya Maine Paakar Kisiko- Lata Mangeshkar (Baradari- Nashad)
74. Umangon Ko Sakhi Pi Ki Nagariya- Lata Mangeshkar (Amar- Naushad)
75. Teer Khate Jayenge- Lata Mangeshkar (Diwana- Naushad)
76. Hame Kaash Tumse Mohabbat Na Hoti- Lata Mangeshkar (Mughale Azam- Naushad)
77. Chal Diye Deke Gham- Lata Mangeshkar (Son Of India- Naushad)
78. Ghar Aaja Ghir Aaye Badra Sanwariya- Lata Mangeshkar (Chhote Nawab- R D Burman)
79. Haye Re Wo Din Kyon Na Aaye- Lata Mangeshkar (Anuradha- Ravi Shankar)
80. Dheere Se Gagri Utaar Re- Lata Mangeshkar (Zindagi Aur Ham- Roshan)
81. Piya Tose Naina Laage Re- Lata Mangeshkar (Guide- S D Burman)
82. Sakhi Kaise Dharun Main Dheer- Lata Mangeshkar (Sangeet Samrat Tansen- S N Tripathi)
83. Bhool Ja Ae Dil Mohabbat Ka Fasana- Lata Mangeshkar (Khel- Sajjad)
84. Gori Babul Ka Gharwa- Lata Mangeshkar (Char Deewari- Salil Chowdhury)
85. Aaja Ri Aa Nindiya Tu Aa- Lata Mangeshkar (Do Bigha Zameen- Salil Chowdhury)
86. Machalti Arzoo Khadi Bahen Pasare- Lata Mangeshkar (Usne Kaha Tha- Salil Chowdhury)
87. Aji Rooth Kar Ab Kahan Jaiyega- Lata Mangeshkar (Arzoo- Shankar Jaikishan)
88. O Basanti Pawan Pagal- Lata Mangeshkar (Jis Desh Mein Ganga Behti Hai- Shankar Jaikishan)
89. Sajan Ki Galiyan Chhod Chali- Lata Mangeshkar (Bazar- Shamsundar)
90. Badalon Barso Nayan Ki Kok Se- Lata Mangeshkar (Sampoorna Ramayan- Vasant Desai)
91. Shri Ramchandra Krupalu Bhaja Man- Lata Mangeshkar (nonfilm)
92. Mere Ansuon Pe Na Muskura- Mubarak Begum (More Man Mituwa- Dattaram)
93. Gesu Ki Purqaif Rangeen Si Fizaon Mein Kahin- Roshnara Begum (Jugnu- Firoz Nizami)
94. Chhod Babul Ka Ghar- Shamshad Begum (Babul- Naushad)
95. Pee Ke Ghar Aaj Pyari Dulhaniya Chali- Shamshad Begum (Mother India- Naushad)
96. Meera Baad Nahin Ab Mane- Sudha Malhotra (nonfilm)
97. Char Din Ki Chandni Thi- Suraiya (Dillagi- Naushad)
98. Bata Ae Asmanwale Tere Bande Kidhar Jayen- Asha, Rafi (Marine Drive- N Dutta)
99. Chori Chori Ik Ishara Ho Gaya Hai- Asha, Rafi (Basant- O P Nayyar)
100. Isharon Isharon Mein Dil Lenewale- Asha, Rafi (Kashmir Ki Kali- O P Nayyar)
101. Saiyan Chhod De Mera Haath- Asha, Rafi (Dev Kanya- S N Tripathi)
102. Baharon Ki Duniya Pukare Tu Aja- Asha, Talat (Laila Majnu- Ghulam Mohd)
103. Ulajh Gaye Do Naina Dekho- Hemant, Lata (Sannata- Hemant Kumar)
104. Chandan Ka Palna Resham Ki Dori- Hemant, Lata (Shabab- Naushad)
105. Aaj Madhubatas Dole- Lata, Mahendra (Stri- C Ramchandra)
106. Kalpana Ke Ghan Baraste- Lata, Mahendra (Amar Jyoti- Vasant Desai)
107. Tum Gagan Ke Chandrama Ho- Lata, Manna (Sati Savitri- Laxmikant Pyarelal)
108. Mere Ae Dil Bata- Lata, Manna (Jhanak Jhanak Payal Baaje- Vasant Desai)
109. Kisi Raah Mein Kisi Mod Par- Lata, Mukesh (Mere Hamsafar- Kalyanji Anandji)
110. Bheegi Palken Utha- Lata, Rafi (Do Gunde- Ghulam Mohd)
111. Sun Mere Sajna Re- Lata, Rafi (Ansoo- Husnlal Bhagatram)
112. Kabhi Raat Din Ham Door The- Lata, Rafi (Aamne Samne- Kalyanji Anandji)
113. Kya Raat Suhani Hai- Lata, Rafi (Alif Laila- Shamsundar)
114. Teri Shehnai Bole- Lata, Rafi (Goonj Uthi Shehnai- Vasant Desai)
115. Jate Jate Ik Nazar Bhar Dekh Lo- Rafi, Shamshad (Qawali Ki Raat- Iqbal Qureshi)
116. Aaj Apna Ho Na Ho Par Kal Hamara Hai- Rafi, Sudha (Kal Hamara Hai- Chitragupt)
117. Magar Ae Hasinae Bekhabar- Rafi, Sulochana Kadam (Dholak- Shamsundar)
118. Meri Zindagi Tere Pyar Mein- Rafi, Suman (Ji Chahta Hai- Kalyanji Anandji)
119. Ham Tumhare Hain Zara Ghar Se Nikal Kar Dekh Lo- Asha, Sudha (Nau Do Gyarah- S D Burman)
120. Marna Bhi Mohabbat Mein Kisi Kaam Na Aya- Ismail Azad, Raghunath Jadhav (Azad- C Ramchandra)
121. Hasi Hasi Panwa Khyaule Gayi Manwa- Mahendra, Manna (Bidesiya- S N Tripathi)
122. Ham Pe Dil Aya To Bolo Kya Karoge- Asha, Rafi, Shamshad (Do Ustad- O P Nayyar)
123. Phir Tumhari Yaad Ayi Ae Sanam- Manna, Rafi, Sadat Khan (Rustom Sohrab- Sajjad)
124. Ho Sake To Dil Ke Badle Dil Inayat Kijiye- Asha, Durani, Rafi, Shamshad (Alladin and the Wonderful Lamp- S N Tripathi)
125. Megha Chhaye Aadhi Raat- Lata (Sharmili- S D Burman)
126. Allah Tero Naam- Lata (Ham Dono- Jaidev)
Note added 9/12/2017: All of these songs are in 14 beats (7 x 2) as follows: 3 + 2 + 2 + 3 + 2 + 2.
However, note the following two songs, in a folk Punjabi taal apparently associated with the popular folk romantic couple Mirza-Sahiban, both found in two different films with the same name, which has 3 + 3 + 2 + 2 + 2 + 2:
Tera Likhanwaliyan- Shamshad (Mirza Sahiban 1947- Pt. Amarnath)
Subah Uthke Mirze Yaar Ne- Rafi (Mirza Sahiban 1957- Sardul Kwatra)
Please also see my blog on Musical Scales (thaat and Raaga):
https://talageri.blogspot.com/2020/02/musical-scales-that-and-raga-i_48.html
https://talageri.blogspot.com/2020/02/musical-scales-that-and-raga-ii_88.html