On Twitter, people do this because of the 140-character limit of their tweet, but URL shortening can have other uses if you are going to use links with your students in therapy. Have you ever tried to ask students to go to a link such as:
That one is an extreme case, but in my experience, even asking a class of typical middle school students to navigate to a website by telling them the URL (or displaying it on the board or screen) will set you up for some frustration. To get all Vygotskian, it's just not in their Zone of Proximal Development to be able to alternate attention between the displayed URL, their keyboard, and their screen in order to monitor their accuracy. And often, students' problem solving ability is limited to directing your attention to the "Not Found" or other website on their screen, rather than checking their entry first. All of this can result in teachers and SLPs feeling frazzled by their lesson and maybe deciding not to use technology next time.
So, URL shortening is one thing to try. If you have a simple enough URL (e.g. enchantedpalace.org), I would say asking kids to enter that in is reasonable. However, if there are a few extra "/s" you're better off shortening.
Try these two: TinyURL and bit.ly. All you need to do is copy and paste your long link, and they will give you a short link to your targeted site. TinyURL has the advantage of letting you customize your link with a meaningful word if you would like, like I did below.
Another newer tool is fur.ly, which lets you shorten multiple URLs into one- so when students enter the one short URL, they are directed to your first entered URL, with a menu bar at the top that allows them to easily navigate to the next site, like my example here: http://fur.ly/1e6y
So try some URL shortening when you are going to be sharing an unreasonably long URL with students- it's a great accommodation for our (and other) kids.