No. I don't support the existence of the International Criminal Court.
What do you propose be done about people like Radovan Karadzic, Ratko Mladic and Omar al-Bashir?
To me, it's about the principle. Sovereignty should be at the level of the nation-state, as should the capability to prosecute and imprison people be. Whatever is or isn't a crime, what the sentence should be, and what the reasoning behind this sentence should be is inherently dependent on the tradition and values in one's own nation-state.
That doesn't make me a cultural relativist: I have no problem saying there's no morality in the criminal justice systems in a lot of countries. However, it does make me recognize that if you have "international" legal experts judge people from completely different contexts based on an "international" (read: American) understanding of whatever is or isn't a crime, the system is there only to re-enforce the authority of the world's big powers and to hollow out smaller nations' sovereignty. There is also no accountability mechanism whatsoever, which is inherent to all these "international" institutions to which power has been silently transferred away.
If a Karadzic or Al-Bashir goes free because this principle needs to be upheld, so be it.