One of the most Googley things about Google has got to be its approach to betas. Much of the software world releases shipping products that should still be beta (or alpha); Google, on the other hand, keeps stuff labeled as beta long after it works so wonderfully well that it's become indispensable.
Google, by the way, sometimes calls its own traits "Googley," but I'm using my own definition here--which is that Googley behavior is contrarian, kind of admirable, possibly self serving, and a tad mysterious, as much (though not all) of Google's actions are.
Anyhow, the Official Google Blog says that Google News, after more than three years, is departing betaland. (It's still labeled as "beta" as of this moment; maybe Google means it'll graduate in the next few days.) It also has a new personalized news feature that--assuming you let Google keep a history of your searches--will add some recommended stories to your news page. (I'm not sure why Google thinks I'll care about some of the stories it's spotlighting for me right now, but I assume that its suggestions will get savvier the more I search.)
As I've remarked before, Google Groups, Google's Usenet service, may be some sort of record-setter when it comes to staying in beta. Unless Google takes it out of beta in the next month or so, I believe it'll have gone a full five years saddled with a moniker that suggests it's something less than fully baked. I'm not sure if Google has grand plans for Groups it hasn't gotten around to implementing, or whether it's unsatisfied with the service as it stands, or what.
The Froogle shopping search engine, which has also been kicking around a long time, is also stuck in beta. Clearly, the Google guys don't believe in social promotions.
As for other Google betas, it's worth visiting Google Labs periodically to see what's in the works.