What metals form ions with a charge of +3, and why?

Iron is the most well-known example, but in fact almost any transition metal, from scandium to gold, is capable of forming 3+ ions.

This is because transition metals, by definition, have d electron shells, which aren't technically considered valence electrons, but nonetheless do participate in chemical bonding, often in quite unusual ways (at least compared to the more typical s and p orbital bonds of alkali metals and nonmetals). If you look at a diagram of the shape of a d shell ("shape" in terms of the region where the quantum wavefunction is strongest), you can see why; they have really weird, complex shapes due to their higher spherical harmonics. The simple models of electron configuration tend to break down in the transition metals for this reason; bonds happen that you wouldn't necessarily expect to happen just from counting valence electrons and looking at electronegativity.