If vaccinated, you will have a greatly reduced risk of cervical cancer. While you can still have an abnormal pap smear after being vaccinated, it is less likely. This is significant since the consequences of having abnormal paps range from inconvenience and expense of having additional minor testing to more serious consequences, such as having biopsies or surgery on your cervix to remove abnormal cells. Biopsies are painful, nothing more, but surgery can jeopardize your reproductive future, complicating future pregnancies.
If you are exposed to HPV and have not been vaccinated, the body's immune system would likely purge the virus on its own and develop immune memory (antibodies) for future protection. Studies have shown, however, that antibody levels that develop naturally are lower than those that develop after vaccination. As for cervical cancer, 4,400 American women a year die of cervical cancer out of a female population of 155 million, so the odds are well against you developing cervical cancer, so long as you are responsible about seeing a gynecologist regularly. Still, cases of cervical cancer still happen, even to responsible women who have regular checkups. But hundreds of thousands of women have abnormal pap smears every year, and that is a much more realistic threat to a woman's health.