Rav Eliezer Cohen
Answer: Since common practices are recognized as valid kinyanim, credit cards and checks as well as online sales would all be considered good ways to transfer ownership in today's society.
We find this concept in the Shulchan Aruch (Choshen Mishpat 202) where a case is discussed regarding a warehouse that sells barrels of wine. When an order came in, the common custom at that time was to mark the barrels that had been set aside for that particular retailer with a specific symbol. Once the symbol had been marked on a barrel, that barrel now belonged to the buyer who had ordered it.
The Shulchan Aruch rules that since this was the common practice, it also worked as a halachic kinyan and the ownership of the barrel was transferred as soon as the mark was made. This concept of accepting common business practices as a valid kinyan is known as situmta.
In today's society, this would apply to purchases made with credit cards and through online sales. Since these are recognized by today's society as acceptable forms of purchase, they would also work according to halacha to transfer ownership as a valid kinyan. In the diamond industry, it is common to seal a deal with the words mazal u'bracha. In fact, even non-Jews use this salutation as a signal that a deal has been concluded. Since this is accepted in the business community, it is a form of situmta and is recognized as a valid kinyan.
Without the concept of situmta, it could be argued that checks would be considered the same as cash, which is not a good kinyan on movable items, or it could possibly be considered like a shtar. I heard one theory that there would be a difference between using a check in Israel and in America. In Israel, it is illegal to place a stop on a check once it has been issued. Accordingly, some suggest that a check has the strength of actual currency, and would have the exact same status as cash. In America, a stop can be put on a check until it is cashed; therefore, it cannot really be considered a form of cash and would have the status of a document that represents a debt.
In any case, in places where it is the common custom to pay with a check, it would have the status of situmata and would be a valid kinyan.
Another application of situmta will be on a davar shelo bah l'olam. Halachically, one cannot purchase an item that is not yet in existence. For example, one cannot buy the crops of a field before they grow. However, the Pischei Teshuva says, that if it is common practice in a certain land for merchants to buy next summer's crops, the sale would be valid because of the rule of situmta.
As we mentioned previously, the Mishpat Shalom goes even further and states that even though Chazal decreed that a cash payment does not constitute a kinyan, if the common business practice is for cash to be used as a means of transferring ownership, in that case it would work as a valid kinyan because of the rule of situmta.
When discussing the laws of kinyanim, the Shulchan Aruch Harav focuses almost completely on the ethics of transactions and barely mentions the different types of kinyanim. I believe that the reason for this is because kinyanim vary greatly depending on the common practices of the time; therefore, he could not give any general rules as to what constitutes a kinyan.