But like I said, we're all very different.
This is true of almost everyone, of course. Every year i read the incoming intern abstracts, and they all literally say the same thing "I really would like to work on <whatever really popular crazy project was in the news lately>". Literally all of them.
That said, often you can work on them if you are good enough at what you do.
(But yes, often you have to prove that first, either internally or externally)
I spent about half my time at Google working on mundane improvements to search - visual redesigns, feature unification, infrastructure improvements - and half working on crazy green-field projects. Most of the crazy stuff was eventually canceled, and the stuff that did launch (eg. Google Authorship) ended up being a lot more toned-down than we initially envisioned. Ultimately I think I learned more from the crazy projects, but it's a very different kind of learning, much more experiential than factual.
The other thing you learn when you actually succeed at a crazy new idea is that people build up a tolerance to them really quickly. The first time we did an interactive doodle on the home page (PacMan...actually technically that was the second, but it was the first people noticed), everybody went wild, it was in all the newspapers, and we calculated people spent 4.82 million hours playing it. Now when an interactive doodle comes out, most people don't even notice. Remember that Google Docs, GMail, etc. were revolutionary in their day; it's only because they've become successful that you don't want to work on them.
But it has other strengths.
working on a giant campus that's isolated from
the outside world
Actually, I am indistinguishable from everybody else.