Google launched vanity URLs or "custom URLs" of you prefer, back in the summer of 2012. They were only available to high profile people like Hugh Jackman at first, but Google expanded them to thousands more soon after.
Now, here in late October of 2013, Google is finally making the URLs available to everyone else. The company announced this in a Google+ post last night, shortly after unveiling some interesting new photo and video features for the Google "social layer".
As long as you have a profile photo, at least ten followers, and an account that is at least 30 days old, you'll be able to choose a URL (google.com/+ChrisCrum, for example). Google says you'll see the option when you visit your own profile. If you don't see it yet, you should sometime this week.
Obviously businesses with Google+ pages are going to want to get their branded URLs. You have to have a linked website or a verified business to claim a custom URL for a page.
"We hope that custom URLs will help you more easily promote your content on Google+, whether it be new photo collections, Hangouts On Air, or an interesting series of posts," Google says.