There are no generic vaccines because vaccines are biologics. Biologics are products that are made using live cells or organisms. The cells or organisms are used to produce certain complex proteins or molecules that are used as medications, and the medications are known as "biologics" or "biopharmaceuticals."
When the patents for regular drugs expire, generic companies can apply to make generic versions. These companies need to submit a little information proving that their product is the same as the brand-name drug, but they do not have to repeat all of the human studies to show the drug to be safe and effective.
Human studies are expensive and time-consuming, and generic medications are less expensive because they do not need all the human studies.
Currently, biologics are governed by a different set of laws. Under these laws, there is no way for a generic biologic to be approved, unless the generic manufacturer completes all of the human studies necessary to approve a brand new drug. Because such studies are extremely expensive, it is likely that a generic biologic would not be any less expensive than the brand-name product.
Essentially, if a generic biologic were to be approved, it would not really be a generic, but a new and separate drug that would not be equivalent to the brand-name product. However, as mentioned, recent legislation has been aimed at changing these laws. It is predicted that new laws and regulations will allow generic biologics in the near future.