How to list the releases of a repository?

I don't think you can specifically do releases. But you can get tags.

curl https://api.github.com/repos/rails/rails/tags

Source: http://developer.github.com/v3/repos/#list-tags

Edit:

They released the releases API today.

http://developer.github.com/v3/repos/releases/

This question is old, however Google still lead me here and the answers are dated. So for any others that find themselves here:

GitHub has sense added a releases endpoint: https://docs.github.com/en/rest/reference/releases

An example of getting one (via curl):

curl https://api.github.com/repos/rails/rails/releases