Hat collecting is the process of gaining rights on Commons (and other wikis) just to show off or to boost one's ego, rather than because you have any actual use for them. Voters in the request for adminship process need to decide whether or not the user requesting adminship actually has a use for those rights or is simply "hat collecting". This is why adminship candidates should have some clear idea why they want to become admins, rather than simply the feeling that this is what one does at a certain stage in one's Commons career.
Not having a particular user right doesn't mean you are somehow deficient. If you are applying for rights, be sure to show why you think you can improve Commons by having those rights, generally by showing a positive record of actions and attitude. Don't just assert that you'll find the tool useful, give evidence of why you need the tool and you'll dramatically reduce accusations that you are simply collecting hats.
Hat collecting can occur across wikis, with users using the rights they've got at one wiki to bootstrap an application on another wiki. This isn't always a problem: most of the user rights require trust.
But remember, some wikis are very lax about handing out user rights. Simple English Wikipedia has been known to hand out rollback after two edits on the basis that the user also had rollback here. Likewise, some rights like autopatrolled or reviewer have many different technical meanings on the various Wikimedia projects, with vastly different associated levels of trust (some higher than here, some lower). Some even automatically allocate extra rights, like the English Wikibooks, which gives out rollback and reviewer by an automatic process. Be careful not to place too much weight on rights on other projects when considering granting them at Wikimedia Commons.