A nucleophile is a species that donates an electron-pair to an electrophile to form a chemical bond in a reaction. All molecules or ions with a free pair of electrons can be nucleophiles. This pair of electrons is called lone pair. Because nucleophiles donate electrons, they fit the definition of Lewis bases. 

Nucleophilic describes the attraction of a nucleophile to the nuclei. Nucleophilicity, sometimes referred to as  nucleophile strength, refers to a substance's nucleophilic character and is often used to compare the attraction of atoms.

Neutral nucleophilic reactions with solvents such as alcohols and water are called "solvolysis". Nucleophiles may take part in nucleophilic substitution reactions. In those reactions, a nucleophile becomes attracted to a full or partial positive charge.

History
The terms nucleophile and electrophile were introduced by Christopher Kelk Ingold in 1929, replacing the terms cationoid and anionoid proposed earlier by A. J. Lapworth in 1925.

The word nucleophile is derived from nucleus and the Greek word φιλος, philos for love.

Properties
In general, within a row across the periodic table, the more basic the ion (the higher the pKa of the conjugate acid) the more reactive it is as a nucleophile. In a given group, polarizability is more important in the determination of the nucleophilicity. In other words, the easier it is to distort the electron cloud around an atom or molecule, the more readily it will react. For example, the iodide ion (I−) is more nucleophilic than the fluoride ion (F−).

Types of nucleophiles
Examples of nucleophiles are anions such as Cl−, or a compound with a lone pair of electrons such as NH3 (ammonia).

In the example below, the oxygen of the hydroxide ion donates an electron pair to bond with the carbon at the end of the bromopropane molecule.  The bond between the carbon and the bromine then undergoes heterolytic fission, with the bromine atom taking the donated electron and becoming the bromide ion (Br−). This is a SN2 reaction occurs by backside attack.  This means that the hydroxide ion attacks the carbon atom from the other side, exactly opposite the bromine ion.  Because of this backside attack, SN2 reactions result in a reversal of the configuration of the electrophile.  If the electrophile is chiral, it typically keeps its chirality, though the SN2 product's configuration is flipped as compared to that of the original electrophile (Walden inversion).  

An ambident nucleophile is one that can attack from two or more places, resulting in two or more products.  For example, the thiocyanate ion (SCN−) may attack from either the S or the N. For this reason, the SN2 reaction of an alkyl halide with SCN− often leads to a mixture of RSCN (an alkyl thiocyanate) and RNCS (an alkyl isothiocyanate). Similar mixtures will happen in the Kolbe nitrile synthesis.

Carbon nucleophiles
Alkyl metal halides are carbon nucleophiles found in the Grignard reaction, Blaise reaction, Reformatsky reaction, and Barbier reaction, organolithium reagents, and anions of a terminal alkyne.

Enols are also carbon nucleophiles.  The formation of an enol is catalyzed by acid or base.  Enols are ambident nucleophiles, but, in general, nucleophilic at the carbon atom next to the carbons with double bond (alpha carbon atom).
Enols are commonly used in condensation reactions, including the Claisen condensation and the aldol condensation reactions.

Oxygen nucleophiles
Examples of oxygen nucleophiles are water (H2O), hydroxide anion, alcohols, alkoxide anions, hydrogen peroxide, and carboxylate anions.

Sulfur nucleophiles
Of sulfur nucleophiles, hydrogen sulfide and its salts, thiols (RSH), thiolate anions (RS−), anions of thiolcarboxylic acids (RC(O)-S−), and anions of dithiocarbonates (RO-C(S)-S−) and dithiocarbamates (R2N-C(S)-S−) are used most often.

In general, sulfur is very nucleophilic because of its large size, which makes it readily polarizable, and its lone pairs of electrons are readily accessible.

Nitrogen nucleophiles
Nitrogen nucleophiles include ammonia, azide, amines, and nitrites.

Related pages
Electrophile
Lewis base

References

Organic chemistry