Goo. gl
Advantages
Analytics
Login is not mandatory
No need for separate login (Google Account)
Powered by The Google
Most reliable URL shortener

Disadvantages:
Duplicate links
No way to remove from listing
Cannot choose the custom URLs
Cannot use custom domain


Bitly
Advantages:
The only thing they do is Shorten Urls
Reliable shortening
Smarter Analytics
Ability to use own domain
Login is not mandatory
Addons and plugins for popular services and softwares
Privatize the shortened URLs
Brilliant sharing
Ability to bundle a bunch of URLs.
Possbility to Archive the URLs

Disadvantages:
No way to remove shortened links from their DB. We need to contact the support staff to remove.