The simple answer to this question is; yes. However, the rates of pregnancy vary greatly depending on what type of birth control you use and how well you use (or how regularly you take) your birth control. Here is a chart that shows the percentage of woman that will get pregnant while on specific types of birth control.
No method of birth control 85%
Natural family planning 1-9%
Sponge (with no previous births) 9%
Spermicide (alone) 6%
Condom (female) 5%
Condom (male) 3%
Depo-Provera Shot 0.3%
Birth Control Pill (Estrogen/Progestin) 0.1%
Mini-pill (Progestin only) 0.5%
As this chart shows, rates of pregnancy vary greatly, but it is possible to get pregnant while you are using birth control. If you do not wish to get pregnant, you can combine methods to increase your chances of not getting pregnant. For instance, you can use a condom with a spermicide to lower your chances of getting pregnant to around 1%. To get the full benefit of birth control you must educate yourself on the proper use of your specific type of birth control.