The Facebookification of Instagram continues today, as the company just added an official feature for tagging people photos. On your profile page, there will be a "Photos of You" section.
Before today, tagging people in Instagram posts worked in the @reply style of Twitter. You could mention people, but you didn't necessarily know whether they were in the photo or whether you were just calling their attention to a post. Now, it works just the way it does on Facebook. As with Facebook, you'll be able to rigorously monitor what photos you're tagged in, as well as the sharing settings for your photos section.
Update: Alright, we got the app update installed on an iPhone. One very disappointing point to note is that the new photos section is empty when you get to it, which means that old-style @reply tags won't be integrated in any obvious way into the new system. That might make sense, since that tool is more akin to a conversational mention than a proper tag.
Otherwise the functionality works more or less as you'd expect. You snap a photo, add your favourite sepia filter, and then head over to the share screen where you will see the option to add people to the photo. And if you forget to add someone, you can always do it from the published post.