Stokes profiles of sunspot penumbrae show distinct asymmetries, which point to gradients in the velocity field and in the magnetic field. We present spectropolarimetric measurements of the Stokes vector in the neutral iron triplet at 1564.8 nm taken with the Tenerife Infrared Polarimeter (TIP) at the German Vacuum Tower Telescope (VTT) in Tenerife. We report on the peculiarities of the profiles of circularly and linearly polarized light for spots at different heliocentric angles. We elaborate on the spatial dependence of Stokes asymmetries within the penumbra and find for profiles of circularly polarized light: (1) In the center-side penumbra the amplitude difference of Stokes-V exhibits a sign reversal on a radial cut, i.e., in the inner (outer) penumbra the red (blue) lobe is broader and shows a smaller amplitude than the blue (red) lobe. (2) In the outer limb-side penumbra (beyond the magnetic neutral line) the red lobe is broader and of less amplitude than the blue lobe. (3) Along the magnetic neutral line we find abnormal Stokes-V profiles, which consist of more than 2 lobes. This indicates the presence of two polarities. For small heliocentric angles abnormal profiles are also seen beyond the magnetic neutral line in the outer penumbra. (4) Maps of the net circular polarization have the tendency to be antisymmetric with respect to the axis that connects disk center with spot center. This finding is striking, because corresponding maps for Fe I 630.25 are symmetric. For linearly polarized profiles we extract the following features: (5) On the center-side penumbra at a heliocentric angle of 56o a Doppler-shift as high as 5 km s-1 can be directly measured by the splitting of the pi -component of the linearly polarized component. (6) In limb-side penumbrae, the profiles of the pi -component show the typical asymmetry properties of the Evershed flow as observed in Stokes-I of magnetically insensitive lines. (7) In the outer center- and limb-side penumbrae the center of the pi -component is blue-shifted relative to the zero-crossing of the V-profile. Motivated by the moving tube model of Schlichenmaier et al. (cite{schlichenmaier+jahn+schmidt1998b}), we construct simple model atmospheres featuring hot upflows and cool outflows and calculate corresponding synthetic V-profiles. These profiles are compared with our measured ones and with observed V-profiles in Fe I 630.25 from other authors. We find that the synthetic V-profiles can reproduce all essential characteristics of observed V-profiles for both lines.