The geometric and the electronic structures, the magnetic moments, and the magnetocrystalline anisotropy energy of bcc-Fe nanowires with z-axis along the (110) direction are calculated in the framework of ab initio theories. In particular, we report a systematic study of free standing nanowires with geometries and sizes ranging from diatomic to 1 nm wide with 31 atoms per unit cell. We found that for nanowires with less than 14 atoms per unit cell, the ground-state structure is body-centered tetragonal. We also calculated the contributions of the dipolar magnetic energy to the magnetic anisotropy energy and found that in some cases, this contribution overcomes the magnetocrystalline part, determining thereby the easy axis direction. These results emphasize the importance and competition between both contributions in low dimensional systems.