I'm a Googler, and comments here from other Googlers are correct: 20% time still exists and requires no manager approval, but only a minority of engineers take advantage of it. For instance, in my team of 14, only 2 work on 20% projects.
I haven't been at Google long enough, but I doubt there was ever a time when a majority of engineers did 20% work. It's hard: you have to take away not only time, but also focus from your main project (which like all software is probably already taking longer to build than you'd like). Most engineers aren't motivated enough.