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A Lewis base is any molecule or ion that can form a new coordinate covalent bond, by donating a pair of electrons. The term base is ambiguous. This is one interpretation. To put it another way, any molecule with an electron lone pair in a bonding orbital may act as a Lewis base, as it is capable of accepting an ion with a single positive charge. Lewis bases are also generally capable of forming hydrogen bonds.
A nucleophile is a Lewis base. Lewis bases do not require a hydroxide ion as the electron acceptor. Some common examples include ammonia and amides. Many anions can also be considered Lewis bases such as F-.
When a Lewis acid and Lewis base form a complex ion the Lewis base is always the ligand.
See also
"Lewis base"