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.