Carriers of today hold 90 aircraft, 2 RAMs, 3 Phalanxs and 2 Sea Sparrow launchers (specs from Wikipedia page on George H.W. Bush aircraft carrier). I'm pretty sure with all this they can defend themselves pretty well.
In comparison, most of the cruise missiles we hear about (Tomahawk for example) are subsonic (though the US does have a few old supersonic ones).
The effectiveness of missile defense systems isn't 100%. It's hard to shoot something travelling at 3600mph. It takes a lot of power, a lot of accuracy, generates a ton of heat, and a requires dash (or two) of lady luck. The defensive system can be overwhelmed for a fraction of the price.