Almost every form of birth has a chance of failure including a tubal ligation, as you might have concluded from the news about the Australian women suing their doctors after they got pregnant with their tubes tied! Only a hysterectomy and total abstinence prevent pregnancy completely. So yes, it is possible to conceive even if you are on the pill. There is a lot you can do to either maximize or minimize your odds, though. It is said that there is a five percent chance of getting pregnant on the pill with "typical use". Compare that to only a 0.1 percent chance with "perfect use".
Perfect use means following the manufacturer's instructions exactly. It means taking the pill every day, at the same time. And it probably also means not continuing the pill for three months to avoid menstrual bleeding. If you have missed a pill, are taking antibiotics, or just want to be on the safe side, use condoms as well as the pill and your odds will go well down! And of course condoms have the added benefit of preventing the spread of sexually transmitted diseases, which the pill doesn't do. As you can see, the chances of getting pregnant on the pill are in fact very small if you use it correctly. Taking your pill in accordance with the manufacturer's instructions is a small price to pay for preventing an unwanted pregnancy, isn't it? But even if you do, it is still possible to get pregnant.