The structure of concentrated temperature-sensitive poly(N-isopropylacrylamide) (PNiPAM) microgel suspensions has been investigated employing rheology and small-angle neutron scattering (SANS). A previously described model expression for the particle form factor P(inho)(q) is extended by a model hard sphere structure factor S(q), and the average radial density profiles phi(r) are calculated from the amplitude of the form factor A(q) and the structure factor S(q). By this procedure, a direct real space description of the spatial ordering in the neighborhood of a single particle is obtained. The overall particle size and the correlation length xi of the concentration fluctuations of the internal polymer network decrease with concentration, revealing the increasing compression of the spheres. Thus, the particle form factor P(inho)(q) of the swollen PNiPAM microgels depends on concentration. The particle-particle interaction potential does not change significantly between 25 and 32 degrees C. Even approximately 1 K below the lower critical solution temperature (LCST), the experimental scattering intensity distributions I(q)/c are described very well by the hard sphere structure factor when an equivalent hard sphere particle size R(HS) and volume fraction eta(HS) are used. Microgels with different degrees of cross-linking and particle size resemble true hard sphere behavior up to effective volume fractions of phi(eff) < 0.35. At higher effective volume fractions phi(eff) > 0.35 strong deviations from true hard spheres are observed. Interpenetration of the outer, less cross-linked regions of the soft spheres as well as particle compression occurred at higher concentrations. In agreement with this, the equilibrium colloidal phase behavior and rheology also has some features of soft sphere systems. At temperatures well above the LCST, the interaction potential becomes strongly attractive and the collapsed microgel spheres form aggregates consisting of flocculated particles without significant long-range order. Hence, an attractive interaction potential in concentrated suspensions of PNiPAM microgels leads to distinctively different structures as compared to attractive hard sphere colloids. When the peculiar structural properties of the PNiPAM microgels are considered, they can be used as model systems in colloidal science.