I use them in presentations, it's easier to have a really short URL on the slide for people. I'm not sure how common that is, but it's really handy. Other than that, I've not used them for anything.

One of the main use cases, and many vendors still do pitch this as a selling point - Analytics. You can put in custom tracking code (www.example.com/landingpage?utm_campaign=xyz&utm_source=abc) and share the same link (eg. a blog post) on different channels (facebook, email, youtube, etc) with different tracking parameters on the fly, so your analytics software can easily pick it up.

I use them to share maps links on chat, for example this:

https://goo.gl/maps/6zJsoaCTgTD2

is much better than this:

https://www.google.it/maps/place/Presidio+di+Francavilla+Fon...

They’re also good for including in SMS text messages. Or print media. Or for typing into browsers on devices with sub-optimal keyboards (from my own experience, I can think of the Xbox and the Kindle)

Situations where a long and nasty url is printed, say in a church bulletin, and so has to be transcribed by eye to be useful.

E.g. imagine a non tech savvy person having to read and type in https://m.signupgenius.com/#!/showSignUp/20f094ea5a928af85-f... to sign up for a church supper.

is.gd/ourchurch-supper2018 is so much easier.

Interestingly, Twitter has it's own built-in t.co URL shortener, so it's not even necessary for that. All links in a tweet are automatically 23 characters.

I use my favorite one just for the laughs: http://www.shadyurl.com

They are good for plain text emails, since a lot of email systems mangle plain text emails at ~ col 72.

On some forums/CMSes bare links to YouTube are converted to full-sized previews automatically and you can't disable this behaviour. You just make a piece of text a plain hyperlink to a YouTube video and once you click "submit" the parser comes into the play and a huge picture appears in the middle of your text instead of a couple of words. Masking the link with goo.gl solves the problem and adds an extra goodie letting you see how many people have followed your link.

Shortened URLs are also easier to type by hand / read aloud and look prettier visually.

Situations where I want users to go to a long URL but they need to type it, or tracking. I want to know how many times my CraigsList ad was viewed, easy I'll just use a short URL for the image and see how many times the image got loaded.

Easier to remember URLs, and statistics about how many people visits them.

At posters, e.g. link to register for an event.

They are easy to share/spell? though most of them are not that easy.