What is the need for so many theories of acids and bases?
First came the Arrhenius theory. It defines an acid as a species that dissociates to produce $\ce{H+}$ in solution, and a base as a species that dissociates to produce $\ce{OH-}$ in solution. (Examples: $\ce{HCl}$, $\ce{NaOH}$)

Next came the Brønsted-Lowry theory, which expands the notion of acid and base. It defines an acid as a species that loses $\ce{H+}$ in a reaction, and a base as a species that gains $\ce{H+}$ in a reaction. All Arrhenius acids and bases are Brønsted-Lowry acids and bases; hence the Brønsted-Lowry theory generalizes the concepts of Arrhenius acids and bases and allows the application of these concepts to a larger range of species. (Examples of "new" acids and bases under this theory: $\ce{NH4+}$, $\ce{CH3COO-}$)

Finally came the Lewis theory, which further expands the notion of acid and base. It defines an acid as a species that accepts an electron pair, and a base as a species that donates an electron pair. All Brønsted-Lowry acids and bases are Lewis acids and bases; hence the Lewis theory generalizes the concepts of Brønsted-Lowry acids and bases and allows the application of these concepts to a larger range of species. (Examples of "new" acids and bases under this theory: $\ce{Li+}$, $\ce{CO}$)



Remark: Hopefully the repetition and structure within my answer has been suggestive. The benefits of generalization are obvious: the theory can explain more, and more things can be explained; this is the natural progression of science.