What kind of anonymization can be used for scanning and exploiting? Of course there are VPNs and VPS, but thats a different story. I know some scanning can be done via TOR, but how can an exploit or something used via proxy?
I am not sure how VPNs will provide anonymity. Even for VPS (in case you meant Virtual Private Server), I am again not sure how will you use that to be anonymous. If you buy a bunch of VPS from linode/rackspace and use it to scan/exploit some servers, it is easy to trace you back. Linode requires a photographic copy of your credit card to activate your VPS.
If you make your scanning programs use Tor, your IP won't be revealed -- but I don't recommend using Tor. Running vulnerability scans using Tor can be really slow. That won't help if you are brute forcing. Also, Tor exit node policies may restrict which ports you can connect to. In addition, it is unethical to use Tor to scan, exploit, or hack other systems.
Expert malicious hackers usually use compromised computers to run their attacks from. They might infect a computer (some university/govt. office) and use that to attack their target, making sure that they have put enough controls that a forensic examination of that computer won't reveal their IP or identity. Again just IP anonymity may not be sufficient in what you are trying to do. Just by visiting a website, you can leave enough evidences to uniquely identify you.
One way to mount attacks from a remote computer is to create a socks proxy to that host and run all the hacking programs using tsocks. Again this is just one scenario and one way... a lot depends on the exact requirements and the tools at hand.
Finally, please do not use these tricks to scan/attack someone without their authorization. Unless you are very thorough, you are bound to leave traces. Whether you'll be found or not depends on how much time and money the other party is willing to spend in the investigations.