Most hosts have this option but it's only available if you have a premium account.
Honestly, unless you are either posting truly hard to find material(And a lot of it!) or are posting brand new content from most major sites every single day, this really won't work as well as you think.
Mostly, people will come to your site, click on a link, get pissed off and then do a google search for the same material using a different host.
Or depending on where you live, you can start up your own file host and then refuse to delete anything if DMCA notices come in.
Doing this is actually pretty cheap. A friend who did this says it cost him a few hundred a month before it was shut down after PP cancelled their contract with him.