Heating ammonium cyanate isomerizes it into urea, a constitutional isomer. Discovery of this reaction in 1828 by German chemist Friedrich Wohler marked the end of vitalism, and the start of modern organic chemistry.
Isomerization at the stereocenter converts the R enantiomer of thalidomide into (S)-thalidomide, its stereoisomer.
Ring flip causes a change in the conformational isomers of methylcyclohexane.
Changing the position of a pi bond and a hydrogen atom results in tautomerization of acetone's keto form into the corresponding enol form.