To get a good idea about the relative paucity of simple Lie algebras (as Mariano says in his comment above), you could take a look at a list of low-dimensional Lie algebras. For instance, here: J. Patera,R.T. Sharp,P. Winternitz, and H. Zassenhaus, Invariants of real low dimension Lie algebras, J. Mathematical Phys. 17 (1976), no. 6, 986–994.