How infectious is Hepatitis B virus?

Hepatitis B virus (HBV) is transmitted by exposure to body fluids, and the common ways of doing this are: via unprotected sex, blood transfusions, needlesticks and from mother to child during childbirth.  It is regarded as highly infectious:

• A needlestick injury (i.e. the patient's infected blood is on a needle, which you then prick yourself with, accidentally [e.g. a doctor] or non-accidentally [e.g. drug users sharing needles]) carries roughly a 30% transmission risk.  Compare this with a roughly 0.3% risk of HIV transmission in the same circumstances.
• A mother who has actively replicating HBV can have up to a  90% risk of transmission to her child.
• HBV retains infectivity when stored at 30°C to 32°C for at least 6 months and when frozen at –15°C for 15 years.
• HBV present in blood can withstand drying on a surface for at least a week.

(The last two terrifying points are from the WHO's page on the HBV.)

So, basically - it's very infectious.