The pairing of spins is often energetically favorable, and electron pairs therefore play a large role in chemistry. They can form a chemical bond between two atoms, or they can occur as a lone pair of valence electrons. They also fill the core levels of an atom.
Because the spins are paired, the magnetic moment of the electrons cancel one another, and the pair's contribution to magnetic properties is generally diamagnetic.
Although a strong tendency to pair off electrons can be observed in chemistry, it is also possible for electrons to occur as unpaired electrons.
In the case of metallic bonding, the magnetic moments also compensate to a large extent, but the bonding is more communal, so that individual pairs of electrons cannot be distinguished and it is better to consider the electrons as a collective 'sea'.