Bundles of semiflexible polymers such as actin filaments are studied theoretically. The bundle formation is governed by attractive filament interactions mediated by cross-linking sticker molecules. Using a combination of analytical arguments and Monte Carlo simulations, it is shown that the formation of bundles of parallel filaments requires a threshold concentration of linkers which becomes independent of the filament number for large bundles. The unbinding of bundles happens in a single, discontinuous transition. We discuss the behavior of the bundle thickness at and below the transition. In the bound phase, large bundles tend to segregate into sub-bundles due to slow kinetics. Our results are in qualitative agreement with experiments on F-actin in the presence of the cross-linking protein alpha-actinin.