Acts 15:19-21, 28 is the Scripture Jehovah's Witnesses typically point to as the reason they refuse to accept blood donations. Acts 15:20 says, "Instead we should write to them, telling them to abstain from food polluted by idols, from sexual immorality, from the meat of strangled animals and from blood." It is clear from the context that the instructions were against eating / drinking blood, not blood transfusions. Blood transfusions were not even possible in Bible times, so there is no possibility that this Scripture could be referring to blood transfusions. There were many pagan religious practices that involved eating and drinking blood and/or strangling an animal to keep more of its blood in its meat. This is what the Bible speaks against, not blood transfusions.
Is it acceptable for a Christian to receive or give a blood transfusion? Since the Bible does not explicitly say, a decision of this nature can only be made between a person and God. One consideration might be that God created billions of people over the centuries, but only four blood types, making it possible to transfuse blood from one person to another, regardless of race or nationality. Perhaps this is an argument for the legitimacy of blood transfusions. A person should carefully and prayerfully consider what God would have him do in regards to receiving/giving a blood transfusion. There is no command either way in Scripture. Blood transfusions are, therefore, a matter of conscience.