If I already own a Domain Name, but did not trademark it... and somebody later trademarks it, can they take then come after me to take my Domain name?

Owning a domain name does not give you an intellectual property right or right to the trademark. If you are using the trademarked words in commerce on your domain, and you were the first to use those words with respect to the goods and services being marketed, you may be able to object to another person obtaining the mark based on common law trademark rights. With that said, if the other party was first, and the other party has a registered mark, it is possible that you  will need to relinquish your domain or simply be required to cease and desist use. There are a lot of factors to consider in this area including whether your site and domain actually infringe the registered mark. Simply having a domain does not mean it infringes and it is possible, especially if you were first, that the mark holder will not be able to force turn over.  With that said, we have forced turnover on behalf of clients who own marks when a domain was acquired and is being used to confuse and interfere with our client's trademark rights.  This is a comples area of intellectual property law and you should obtain the advice of a lawyer with knowledge and experience in e-commerce, intellectual property and UDRP procedures.