With Google+ continuing to grow more and more short URL services are becoming available. The issue today is that telling someone your Google+ profile internet address is near impossible with the pertinent part being a long number mine is 106507463771539639056.
Facebook, Twitter, and LinkedIn were all purpose built for social networks and easily allow you to append their base domain name with "/username" to get to someone's profile. Google, as we all know, started as something else and allowing this same functionality is apparently not as simple. The closest you can officially get today is if you had set up a shorter link when Google Profiles were a stand-alone product before G+ came along. For example, I set mine up to be profiles.google.com/dbin78 which now directs to my Google+ profile.
I personally find no need for a short "vanity" URL. Using normal shortening services like bit.ly and goo.gl work fine for my needs, which are for space saving and aesthetics online. Linking on a website or in an email signature can all be done with simple coding/formatting where the link and visible text are different.
Many people like having a username branded short link, and it is really needed when something is in print or on TV. Until Google launches a feature to accomplish this (maybe using g.co?) we must seek outside help or search for a user. After testing and researching many different services I recommend these three services based on reliability, trustworthiness, domain data, ease of use, and other elements.
Topl.us - Simple and fast just enter your desired username and Google+ ID number to create a short URL that looks like "topl.us/username".
PlusYa.com - Analytics are baked in with this shortener. After selecting your nickname and connecting to your Google account through OAuth you are brought to a dashboard where you can track the clicks on your link, "plusya.com/username". By not manually entering a Google+ ID you are ensured short URLs with this service are not being created without the user's permission.
onGPL.US - Basic and reliable! After selecting a name and linking it to your G+ profile you are provided with a URL formatted as "ongpl.us/username".