Jawbone has a competing product, and even Samsung Galaxy S4's latest phone includes some of the functionality (ie: a pedometer) people look to Fitbit for.
My anecdotal experiences with GS4 vs my Fitbit One shows the Fitbit One to be superior, but I'm more likely to forget my Fitbit than I am to forget my phone.
iPhone has an app called Moves which is remarkably accurate (http://www.moves-app.com/). I'm getting fairly similar results from my jawbone. I believe the discrepancy is due to the fact that I don't have the phone on me when I'm at home.
Yep, as others have said, Nike Fuelband (I own one, as does my wife), Jawbone, a variety of iOS and Android apps. Tons of new Kickstarter projects, etc.
