On another note, rebinding ctrl-c, ctrl-v, ctrl-s etc. in the terminal (including Vim) can be confusing, since most ctrl commands will be caught by stty (in most terminal emulators) and never passed on to the running application. If you really wanted to, you could rebind Vim's yank/paste to ctrl-c, ctrl-v by unbinding the stty commands.

  # 1. check the bindings for your system
  stty -a
  # 2. put the stuff you want to unbind in your shell rc file
  stty <command name> undef

And then rebinding yank/paste in your .vimrc to only use your system clipboard.

This would, however, become painful as soon as you need to quickly use a machine remotely where all your local configs won't be present. It also generally raises the question why one is using Vim in the first place, if one is not planning to use its powerful features.