Typical non-nucleophilic bases are bulky, such that protons can attach to the basic center but alkylation and complexation is inhibited.
A variety of amines and nitrogen heterocycles are useful bases of moderate strength (pKa of conjugate acid around 10-13) Non-nucleophilic bases of high strength are usually anions.
These compounds are dense, salt-like materials that are insoluble and operate by surface reactions.
Some reagents are of high basicity (pKa of conjugate acid around 17) but of modest but not negligible nucleophilicity.
The following diagram shows how the hindered base, lithium diisopropylamide, is used to deprotonate an ester to give the enolate in the Claisen ester condensation, instead of undergoing a nucleophilic substitution.