The iPad/Arduino powered Kegmate at Yelp[1] is the result of a Hackathon, which are regularly scheduled. The most recent one was expanded to two days because we found that one day just wasn't enough. It's a lot of fun and many people work straight through to power through implementing their ideas. A lot of interesting, good things have come out of these events. You can work on anything, you need to present it to all the other engineers at the end, and we encourage you to work with people from other teams that you might not normally get a chance to work with. For weeks before hand, people are coming up with ideas, drumming up support/finding other people who are interested in the same idea to work with, and judging effort to make sure they are working on something can be demoable at the end. I got a chance to get involved with doing some embedded development, which I'm interested in but don't normally get a chance to work on.
There's been a lot of fun things, and a lot of productive things. From Kegmate to a MUD that simulated the office environment to unexpected reporting tools that help out other departments.
Can you spend your Twitter/Google 20% time doing something non-technical that matters to you or your community? Like helping out a local charity, drinking beer, or gardening for your disabled neighbour?
I don't work at Google, but when I interviewed there I asked a similar question and they said something like "your supervisor should be consulted about what you work on". So I bet not.
Note that one week a year is actually... 2% time. A full 20% would work out to about 2 and a third months a year. Regular "hack" time and private project time is good, but 20% time is so quantitatively different that it's fundamentally qualitatively different as well.
Except this is probably worse - there is an end-of-the-week show and tell! Engineers always come up with very cool yet non-trivial ideas. And as with almost all software projects, the last few days before show and tell will be crunch time - either to simply get it running, or to add those last few cool features.
There's been a lot of fun things, and a lot of productive things. From Kegmate to a MUD that simulated the office environment to unexpected reporting tools that help out other departments.
[1] http://engineeringblog.yelp.com/2010/08/yelp-makes-beer-more... (previously posted on hacker news)