Alkali metals chemistry
Maurice notes that alkali metal diatomic molecules are at best a very minor constituent.  But alkali metals do fill their $s$ valence shells in other ways.

Most alkali metals are known to form alkalides, in which an electron is transferred from one alkali metal to another (or from barium to an alkali metal, in a more recent example).  To effect this electron transfer, a complexing agent is used to stabilize the cation, such as 2.2.2 cryptand in the compound $\ce{[Na}\text{(2.2.2-crpytand)}\ce{]^+Na^-}$.  A combination of low ionization energy, positive electron affinity and the stabilization offered by complexing the cation enable this outcome.

Lithium apparently fails to form such alkalides, but not because it refuses to adopt an $s^2$ valence electron configuration.  Quite the opposite: it tends to form polar covalent bonds with that configuration.  Organolithium compounds are a widely used example of this electron structure, and the covalent bonding component in lithium salts may contribute to their solubility in some organic solvents.