I think that shortening your url using link shortening websites will affect your websites SEO. The reason being, this will decrease the number of websites linking to the page the short url is linking to. Am I right? Any website linking to the link of the shortened link is actually linking to the url shortening website before it redirects to your website So I think link shortening is not good especially when your search optimizing your website. I don't have a lot of knowledge on how link shortening websites work so I might be wrong.
If You are using WP you can use a plugin like Gocodes. That way you aren't reliant on a web service like budurl or tinyurl. If they change terms of lose your data then your links are gone. Hope this helps.