Somewhat related to Igor Pak's comment is the classification of the finite irreducible Coxeter groups. Of course they are not "simple" as groups, but the irreducibility seems the natural replacement for simplicity; here "irreducible" means that the Coxeter diagram is connected, or equivalently, that the Coxeter system does not split as the direct product of two Coxeter systems.
The outcome is the famous list $A_n$, $B_n = C_n$, $D_n$, $E_6$, $E_7$, $E_8$, $F_4$, $G_2$, $H_3$, $H_4$, $I_{(n)}$, where the last three items are maybe less well known people only familiar with Lie groups and Lie algebras and/or algebraic groups since they don't survive there.
