Dear do do doer,
More than likely float up against the ceiling when inside, but float out into deep space otherwise. Of course, there's no telling, with all the building collapses in the news nowadays, how many buildings would take off, as rubble, into deep space as well. So you might bump into a ceiling and then fly off into deep space with the building you just smashed into.
At 600 to 1000 mph rotation speed for Earth, where people live the most, you, me, and my dog Boots are being subjected to centrifugal force that wants to throw us up and out. Only gravity prevents that from happening. [See source.]
Without the gravity...bye bye.
The centrifugal force at a given latitude is found from F = ma = m W^2 R cos(LAT) where W = 2piF and F = 1 cycle/24 hrs = 1/(24*3600) cps is the rotation frequency. R = 6371E3 m is Earth's radius. m is your mass and LAT is the latitude you live at. Plug in the numbers and you'll see how much centrifugal force is acting on you right now.
EX: F = 100*(2*pi()*(1/(24*3600)))^2*6371E3*cos(... = 2.165745165 = 2.166 N. Is the centrifugal force on me at LAT = 50 deg N. At m = 100 kg, I would accelerate A = F/m = .022 m/s^2 off the planet should gravity cease. (Of course, so would the air leave as it's normally held by gravity; so I'd suffocate long before reaching any significant height off the surface.)