Eat your own dog food
Your test cases are the first users of your API. Many things become only really clear when playing around with the API a bit. It is a huge benefit for the API’s usability.
Build confidence of your codebase
Sooner or later, without proper testing, you will loose confidence in what you built. That is because there will be bugs. This is perfectly normal and OK. But without proper testing, you will just fix those bugs somehow and hope for the best. That will destroy your confidence in the code because all those bugs will give you the feeling that the complete codebase is just a big pice of crap. What you should do instead is to welcome each new bug and answer to it by writing a few test cases. This will cause new bugs to increase your confidence of the code instead of decreasing it.
Seeing all green
Last but not least, Seeing all green will become a huge satisfaction!
.. work in progress..