The lag basically kills it for anything "serious" that requires precise timing and reaction.
I tried playing New Super Mario Bros once at a friend's place, and their HDTV's processing introduced lag, which made it pretty much unplayable (missed jumps, enemies/projectiles hit by mistake). After we were about to give up, we discovered that the TV had a special game mode, and then it was fine.
Unfortunately for Kinect there's no button to press (hah!) to turn off the lag.
"Well certainly with the Xbox 360, we had some challenges at the launch. Once we identified that we took control of it. We wanted to do it right by our customers. Our customers are very important to us." -Larry "Major Nelson" Hryb (10/2013). Note: RRoD was fixed with the Jasper-revision 3 years after the launch of 360
"People don't pay attention to a lot of the details."-Yusuf Mehdi explaining why Xbone DRM scheme would succeed
"Fortunately we have a product for people who aren't able to get some form of connectivity; it's called Xbox 360,”-Don Mattrick
"The region locking of the 3DS wasn't done for profits on games"-MDMAlliance
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