We bought one for Christmas and have basically been playing it non-stop.  It's amazing.  And, we've been completely satisfied playing just the game that comes with the Kinect (which is an adventures-type game where you can do lots of different things, like white water rafting, dodge ball-type thing, flying in space, etc).     
We also have a Wii.  The Kinect is, IMHO, much better.  The technology is just better, which makes for a cooler gaming experience.     
I'm not what you'd consider a "hardcore" gamer.  In the past year, I've played the Kinect, Deadrising 2, and on the Wii.  That's it.  So, take my feedback for what it's worth (which isn't much, probably!  ).     
I have an old XBox 360 - like I bought it when it first came out.  I have done nothing to it (i.e., I haven't done any of the modifications or whatever that you can do).  To play the Kinect, I needed two additional things that I didn't have: (1) a flash drive for more memory and (2) to connect to XBox Live so that I could download an update, which took like 15 seconds to download.  That was it.     
Hope this was helpful.  Let me know if it wasn't.