Best-known for the slogan, "the urge to destroy is a creative urge" (as in, "I want to create some smashed glass from that McDonald's window over there") - very much a spiky. The basic idea here is that clearing space occupied by existing (violent) relations is necessary to create the possibility of a new, liberated world.
God and the State is a strongly-worded attack on Christianity for enshrining the idea of unequal power in metaphysical absolutism. "If God existed we would have to overthrow Him". "A boss on heaven is a good excuse for a boss on earth". Bakunin is a strong materialist, one of a number of similarities with Marx.
In Statism and Anarchy, he analyses international relations from a perspective which, in common with conventional IR Realism, maintains that states are inherently violent and try to take over as much territory as possible, but which, unlike IR Realism, uses this as a basis to condemn the state.
His critique of Marxism is based on its alleged authoritarianism, especially in terms of the idea of dictatorship of the proletariat. He claims that Marxian socialism would inevitably degenerate into a dictatorship by a small stratum of intellectuals and bureaucrats because of its centralism and its lack of support for grassroots activity; also that the better-off workers would rule at the expense of the "lumpen-proletarian" (socially excluded) poor and the peasants. Marx and Engels try to rebut these claims in various essays, accusing the Bakuninists of taking a dogmatic approach to political action and of succumbing to bourgeois nationalism.
Today, his work is popular with both anarcho-communists and green anarchists, although they do not usually adopt his peculiar ideas on organisation (emphasising small numbers of professional revolutionaries as a catalyst for a movement which was nevertheless to be popular and mass-based) or his personal prejudices.
Down-sides to Bakunin's work include his nationalistic chauvinism and anti-Semitism. Also, he didn't clarify his own theoretical ideas; most of what he wrote is either short pamphlets or is incomplete.
Stop spouting all that right-wing shit, or I'll do a Bakunin on your ass.