This question can be approached from different perspectives.
First is the is what the law of the land is. Although halacha does not always follow secular law, in questions of business conduct we are obligated to follow the law of the land, which we know by the term "dina d'malchuso dina." On this, Rav Yitzchak Shmelkes (Beit Yitzchak, Yoreh De'ah 2:75) wrote, "I am not aware of any Torah source that prohibits copying a Torah work without the authority and permission of the author." However, he states that one must obey copyright laws that the civil government enacts due to the Talmudic rule of "dina demalchuta dina." This rule, literally, "the law of the government is the law," obligates Jews to follow many laws of the land in which they dwell. So, if secular copyright law makes it illegal to make and sell imitation products, then that is reason enough for Jewish law to forbid trading in such illegal items. Note that these days copyrights extend not to just works of writing, but to designs, music, and computer programs, for example.
Second, we want to avoid participating in a fraud. If the seller is selling a Rolex for $250 on the street, its either fake or stolen. Selling things under a famous trade name, when they were not manufactured by that company, is a violation of the Biblical principal of "ona'ah" (cheating someone in business). Lev. 25:14 ("And if you sell anything to your fellow or buy anything from your fellow’s hand, you shall not wrong (AL TONU) one another"). See Bava Metzia 49b - 58b. Likewise, buying knockoffs is also forbidden, even if you personally know they are imitation, as you are supporting the sinner's activity.
But a different case would be if a manufacturer made something that looked similar but not identical to a more expensive design, and did not claim it to be anything other than what it is. For example, when my wife and I were getting married, we registered for a china pattern that was similar to a Royal Daulton design we liked, but made by Mikassa and noticeably different than the Royal Daulton so much that they could not be confused. Since we paid the value of a Mikassa and not a Royal Daulton, the transaction was totally honest and there was no issue of "ona'ah."
Getting back to the Rolex watches for sale cheap, I mentioned that there is a possibility that instead of being fake, it was stolen. Where one has reason to believe that the goods are not imitation but stolen then it is forbidden to buy such objects (see Shulchan Aruch, Choshen Mishpat 366.1). Even if this is only a suspicion (but one based on good assumptions, such as the price is incredibly low, or its being sold in a suspicious way etc) it is also forbidden to buy it (see Taz ibid).
