Why do humans drown in water? If humans have a density of 985Kg/m^3, then why do humans drown as water has a density of 1000Kg/m^3.
 A: Besides the fact explained in Steeven's comment, there is also the fact that the density of the human body with little air is not so small.
The average density of human body with maximal expiration is in general greater than the density of water, even for bodies with considerable amount of fat (check some nice tables here). The main sources of variation in the average density of human body are the amount of air in the lungs (1 to 6 or 7 liters) and the amount of gastrointestinal gases (up to 2.5 liters). Such variable volume can easily allow a regular person to sink with empty lungs and to float with air full lungs.
Based on the tables cited above, let us consider an adult male with 75 kg and about 27% of body fat (that would be a regular guy). Neglecting residual lungs volume, i.e., no air, this person has of about density 1.04 g/ml, which gives volume
$$V=\frac{75000}{1.04}=72,115.38\, ml=72.12\, l.$$
At his maximal exhaling he will have about 1 liter of air in the lungs, so his volume increases to $73.12\, l$ and his average density becomes $1.03\, g/ml$. It still sinks.
Assuming that at his maximum inhale his lungs occupy 4 liters, then his density will be 
$$\rho = 75/76.12\approx 0.99\, g/ml,$$
and he floats.
A: Our bodies generally are neutrally buoyant when we exhale. Variations on the density you cite exist depending on difference in tissue masses of individuals. Fat is more buoyant than muscle mass.
Survival outcome in a potential drowning situation can depend on the depth/timing of breathing.  Panicked breathing can be rapid, shallow, and screaming just empties the lungs causing an immediate loss in buoyancy. By deeply filling the lungs and maintaining a slow breathing rate with relatively high I/E ratio the lungs themselves can serve as a source of buoyancy, at least in calm water. But not so easy in a heavy sea.
Survival training will teach the above technique and back floating to keep the mouth and nostrils clear of the surface. Panic is the killer and so these techniques should be practiced before an actual survival situation happens.
