We studied the adsorption of single atoms on a semiconducting and metallic single-wall carbon nanotube from first principles for a large number of foreign atoms. The stable adsorption sites, binding energy, and the resulting electronic properties are analyzed. The character of the bonding and associated physical properties exhibit dramatic variations depending on the type of the adsorbed atom. While the atoms of good conducting metals, such as Cu and Au, form very weak bonding, atoms such as Ti, Sc, Nb, and Ta are adsorbed with relatively high binding energy. Most of the adsorbed transition-metal atoms excluding Ni, Pd, and Pt have a magnetic ground state with a significant magnetic moment. Our results suggest that carbon nanotubes can be functionalized in different ways by their coverage with different atoms, showing interesting applications such as one-dimensional nanomagnets or nanoconductors and conducting connects, etc.