URL shorteners such as bitly, ow.ly, buff.ly are created to shorten blog articles super long URLs when sharing to social media platform that requires limited number of characters such as Twitter. Link shorteners are also have their own click tracking features that is way more advanced than other analytics which means you can pinpoint where the clicks are coming, how many click per day, what link are the most clicked and so on.
Other utilized shorteners when they are doing affiliate marketing to hide the referral link which they believe that can affect the conversion rates of their sales. This is not considered as illegal as you are just trying to minimize the super long URLs. Other link shorteners also allows custom domain or cname so that you can use your own domain name instead of the providers domain name to display your own branding. These services charges a small amount because of the additional functionalities, but you can definitely use the free services without any problem. The only thing that I have found out with free services – there is a limit on page views that it can accommodate.
So if you are looking for a URL shortener, check out the links I’ve mentioned above and you can try each one of those and stick on the one that you prefer. I also want to add that Twitter now somehow can shorten long urls on its own using t.co domain name.