Curse preceding/leading to birth is such an abundant motif in Indian narratives that the list may easily run into a few hundreds.
Particularly because your range is so big, no bar on tradition or period. That makes it various forms of folk narratives such as fairy tales , legends etc. get included.
Just in myth-lore or mythology itself the list is very big.
The abundance of this is so big that I would imagine that it could have been the main or part focus of several researches and/or publications.
I have been using a word meta-myth to refer to myths 'explaining' or linking or connecting myths. Narratives of curse leading to birth or incarnation are one variety of such myth-explaining or myth-linking myths.
One very popular and significant instance of this is the curse to Jaya and Vijaya , the dvaarapaalaka-s of VaikunTha , to be born as Asuras in three different births. In the first, they are born as Hiranyakasipu and Hiranyaaksha. In the second, as RaavaNa and KumbhakarNa. In the third as S'is'upaala and Dantavaktra. The significance of this is that this narrative is key to the concept of Vaira Bhakti = devotion in the form of enmity.
This I group under myth-explaining myths. Explanation in this case is vaira bhakti. Ramayana versions without the narrative of Jaya and Vijaya included or without the descrition of RaavaNa and KumbhakarNa as born due to curse, do exist. So we can say versions of Raama-RaavaNa story with the curse of Jaya Vijaya included can be seen as narratives explaining the version of the narrative without the curse aspect. Bhaagavata is the Purana which gives significance to this curse narrative.
The post is already long.
This can go on and on.
I am sure almost every member remembers one or the other stories from Puranas and Itihasas.
What I can add is from folk narratives.
To see how medieval Indian poets exploited this for creating new narratives of great poetic skill, read the 16th century Telugu narrative epic poem Kalapurnodayam. I called the story of this as utpaadyapuraaNakatha in my PhD dissertation. English translation of this poetic work by Prof's David Shulman and Velcheru Narayana Rao is called "The Sound of Kiss". Available to buy.
A huge and interesting area to explore if not explored previously.
Best wishes,
-N