The interaction of 3d transition metal atoms and dimers with a single-walled armchair carbon nanotube has been investigated by first-principles density functional calculations. For Fe-, Co- and Ni-doped (4,4) nanotubes, outside adsorption sites are the most favorable. The interactions are largely ferromagnetic for Fe and Co, with the local magnetic moments of the dimers being similar to the free dimers. However, for Ni most structures are nonmagnetic. We have also examined the effects of curvature with calculations for graphene and the (8,8) nanotube. For the (8,8) nanotube, the interaction of Co becomes more favorable inside the nanotube. Doping of a single Co atom transforms the (4,4) and (8,8) nanotubes into half-metals. These results are useful for spintronics applications and could help in the development of magnetic nanostructures and metallic nanotube coatings. {\textcopyright} 2004 The American Physical Society.