Imagine a situation where I register a company "Asdf". Now, Asdf.com already registered (some 5 years ago). I have all the other major variations of Asdf (.net, .org etc..). Now that I have a registered company and I have a trademark for "Asdf" can I claim that the .com should belong to me? Would this stand in court? Has anybody faced this before?
Requirements to take a domain: The domain name is identical or confusingly similar to a trademark or service mark in which the complainant has rights; The registrant does not have any rights or legitimate interests in the domain name; and The registrant registered the domain name and is using it in "bad faith". http://en.wikipedia.org/wiki/UDRP Because they registered the domain before you had a trademark, you will be unable to prove that the domain was registered in bad faith.
Other than what xtmx since answered, a trademark aims to prevent consumer confusion. It's not intended to necessarily grant some magical claim towards any and all domain namesakes for any and all other uses. Some have tried, nonetheless. Very, very few succeeded AFAIK, and it's probably because their domain owners just couldn't realistically fight or had an extenuating circumstance against them. The others that also tried pulling this off, lost. At the top of my head, search online for the mess.com dispute and GoForIt vs. DigiMedia.