Metal-semiconductor contacts play a key role in electronics. Here we show that for quasi-one-dimensional (Q1D) structures such as nanotubes and nanowires, side contact with the metal only leads to weak band realignment, in contrast with bulk metal-semiconductor contacts. Schottky barriers are much reduced compared with the bulk limit, and should facilitate the formation of good contacts. However, the conventional strategy of heavily doping the semiconductor to obtain Ohmic contacts breaks down as the nanowire diameter is reduced. The issue of Fermi level pinning is also discussed, and it is demonstrated that the unique density of states of Q1D structures makes them less sensitive to this effect. Our results agree with recent experimental work, and should apply to a broad range of Q1D materials.