I have several backlinks from quality sites that link to something like "http://site.com/gobbledygook/http://mysite.com when I hover over the link. And sites like Twitter do the whole url shortening thing. So my question is, as long as the link is not 'nofollow' am I getting a valid backlink with link juice?
URL shortening services usually use 301 redirection (the most popular services do at least).
If they do so, you will get most of the link juice.
However some might not use that type of redirection. In order to check that you can use programs like curl (UNIX):