- It adds a redirection delay.
- If the company/server providing the service goes down, all your shared short links are dead.
- Problematic for your link juice (aka SEO)
- A third party is keep tracking of traffic data to your web page through its url shortener service which can be used in some ways I might not like.
In case of Google, I am already trusting it with lot of my data in the form of my emails, website analytics, adwords, docs etc. so giving it so some additional information through goo.gl is not something to worry for me.
Possibility of Google going bankrupt is also very remote (And if it does happen, I have other things to worry than my dead links)
With its own URL shortener, Google can take care of any link direction directly from its search engine as well as any SEO issues. (I have not done any research or experiment and this is just my hunch feeling.)
I try to avoid url shortener whenever possible but tend to trust goo.gl a little more than any other url shortener.