Not really. This article does a decent job of discussing the topic. In short, it is theoretically possible that certain cancers could be "transmissible," but the subject isn't very well understood. However, a big study of medical registry data in Scandinavia found no statistically significant increased risk of cancer among people who had received a blood transfusion from someone who developed cancer.

Key takeaway is here:

>The researchers identified 978 cases of cancer among all the blood recipients but after statistical analysis they found no excess risk of cancer overall among individuals who had received one or more blood products from a precancerous blood donor. The relative risk was not substantially affected by sex age, calendar period, or number of transfusions. What is more, there was no excess risk when patients who received blood from people with cancers at sites that are thought to have the highest risk of metastasising through blood---the lung, liver, skeleton, and central nervous system---were combined.

Similar studies in the US have found the same thing: "Results did not imply any concrete association between cancer risk and history of blood transfusion. These findings would help in debunking the myth of increased cancer risk following blood transfusion."