How can I remap CTRL-h in Mac OS X?

The default ⌃H behavior comes from the Standard Key Bindings file in the AppKit framework resources. You can override this easily.

Create a file with this as the contents:

{ "^h" = ""; }

And save it to ~/Library/KeyBindings/DefaultKeyBinding.dict, creating the KeyBindings folder if it doesn't exist. (Note: you will need to restart your applications for this to start working.)

(Another side note: I'm not entirely sure if using "" is the right way to make it do nothing, but it works. The documentation I found said nothing about any no-op methods.)

DoubleCommand will let you do this.