If you are talking about link that you published to other people's websites, you are stuck with short URL services I am afraid.
The shortener services track the use of your link by redirecting them through a script that monitors traffic. That is what you get reported back. If the links are direct then you don't get that tracked, so no data to report.
You could work around that by setting up your own redirect script. You'd then post your own URLs and get them to redirect, picking up the data on the way. Quite easy to write, but I am sure that someone will have already written this and made it available somewhere online.
If the links are to your own pages anyway then you can use analytics to monitor their use. Using campaign tracking variables on the link will let you track particular posts.
Other than that you are stuck with the metrics provided by the places that you post the links. Those are not that helpful I know.
What is the particular problem with the likes of bitly? What are they not given you that you need?