Can I register a URL that's a twist on a famous corporate name?

If the domain name is one that's intended to confuse consumers of the company or if it's the same (or substantially similar) to that of the well known company, you'll most likely have to give it up. You will either be infringing (confusing consumers as to the source), diluting (diminishing the power of a famous trademark), or cybersquatting (acquiring a domain name in bad faith -- for example to sell it back to the company), all of which will get you in legal hot water. In addition to facing a domain name arbitration or federal court injunction, you may be held liable for costs and possibly attorneys' fees.