Is it true that men have one more rib bone than women and if so, how many do each of us have?

Very interesting question.  Strictly speaking from an anatomical perspective, both males and females only have 12 pairs of ribs (24 single ribs).  The ribs begin in the thoracic spine region.  There are twelve thoracic vertebrae and a rib attaches to each vertebrae forming the back of the rib cage.  In front, the first 7 pairs connect to the sternum by cartilage and are known as “true ribs.”  The remaining 5 are called “false ribs”.  The 8^th – 10^th rib usually share a cartilage attachment and do not individually attach to the sternum.  The 11^th and 12^th ribs do not attach to cartilage and thus are considered “floating ribs”.

There are occasions when males and females possess an extra rib. When this occurs, it is usually known as a cervical rib since it attaches to the 7^th cervical vertebrae.  Cervical ribs are present about 0.5% of the population and are twice as common in females.  They are bilateral in 66% of the cases.

References:
Standring, S (2005) Gray’s Anatomy: the anatomical basis of clinical practice, pp. 955.  Elsevier, New York.

Yochum, T and Rowe, LJ (1996) Essentials of Skeletal Radiology, pp. 220. Lippincott-Williams and Wilkins, Baltimore.