Tiny.ee is my main project. The one that I pour countless hours into maintaining and growing.
It has been the most successful by far, with it only being 2 years old (technically still a baby).
It's free to use and you can create an unlimited amount, whether it is through the homepage directly, or using the API available.
Not only can you generate random url suffixes, but you can also choose your own, for example tiny.ee/extension - that was created using the shortening service which then redirects you to the Chrome store (be sure to have a look at the plugin).
At the time of writing this post, the global ranking of Tiny.ee is: