What risks are associated with a biopsy?

Very limited: Bleeding, infection, tracking and nerve damage are the most frequent complications, although very rare. Depends on what is being biopsied and how: brain with a craniotomy is very different from a fine needle aspiration of a soft tissue lipoma (fatty tumor). If it is under radiology guidance (ct or us), a lung collapse is possible. So, while site dependent, you are probably going to be just fine.