It is difficult to say precisely what current would pass through your body if you were to touch the terminals of a 9.0 V battery with your hands. There are a number of factors that would influence the actual current:
Your body's resistance - The resistance of your body depends on factors like skin moisture, calluses on your hands, and even how recently you have exercised. Dry hands with calluses have higher resistance, while sweaty hands have lower resistance.
Touching the terminals - The exact area of contact with the terminals and how firmly you grasp them will affect the current. Larger contact area and firmer grip leads to higher current.
Length of contact - The longer you touch the terminals, the higher the current will likely be as your skin resistance decreases over time.
Health of the battery - A new battery with full charge will provide higher current than one that is partially drained.
In general, for a healthy person with average resistance (around 1000 ohms), touching 9 V battery terminals briefly could result in currents on the order of milliamps (a few mA). However, due to the many variables at play, the current could potentially range from around 1 mA up to 10s of milliamps depending on factors like those listed above.
For reference, currents above 50-100 mA can start to cause involuntary muscle contraction and difficulty letting go. However, the 9 V battery's relatively low current capability makes severe injury unlikely in most cases. The main risks are minor shock and burns from the contacts.