The article "Infectious and immunologic consequences of blood transfusion", in Critical Care June 2004 Vol 8 Suppl 2, stated under the heading, "Infectious risks of blood transfusion":

"Any intravenously administered fluid can transmit infection, but blood is a uniquely nutritious medium and is seemingly an excellent means for transmitting infection. In fact, any pathogen that is capable of existing in blood can be transmitted in this manner. It is a tribute to modern blood banking procedures that transfusion-transmitted infection is actually quite rare. Blood-borne parasites can be transmitted with transfusion, and a handful of cases of malaria, babesiosis, Chagas’ disease, trypanosomiasis, and toxoplasmosis have been reported. The primary means of preventing these infections is through careful screening of donors, especially those who have traveled to areas that are endemic for these diseases. Syphilis can be transmitted by blood transfusion but no cases have been reported since 1969; it is generally thought that the practice of refrigerating blood, which kills spirochetes within 1–2 days, is responsible for this. Bacterial contamination is the second most frequently reported cause of blood transfusion-related death after hemolytic reactions, and it accounts for more than 10% of transfusion-associated deaths in the USA."

The article goes on to discuss the risk viral infections, such as hepatitis C and HIV being transmitted by blood products and shows the these risks have been significantly reduced in recent years through a rigorous and costly screening program.

However, no amount of screening will eliminate all risks of disease transmission through blood transfusion and, in addition to diseases, there is the possibility of transfusion-induced immunomodulation (the suppressing of the patient's immune system) [see Transfusion Practice: Allogeneic blood transfusions explain increased mortality in women], due to the presence of antibodies and white blood cells in donor blood. Another serious problem is TRALI (transfusion-related acute lung injury). [See Transfusion-related acute lung injury (TRALI) A clear and present danger]

Thus, while the risks of blood transfusion may seem to be small, taken separately, there is an aggregate risk with each transfusion event, which can be serious enough to be life-threatening.