Virtually all cervical cancers come from HPV infections. There are many, many, many strains of HPV, though only a few are at high risk to develop into cervical cancer.
The HPV vaccine you hear about vaccinates against the two strains that are responsible for 70% of cervical cancers. It also targets several that form less than appearling warts (i.e. condyloma accuminata).
The problem is that the "warts" of the strains that cause cancer are very small and very easy to miss. Just because you don't see warts doesn't mean that you don't have HPV.
That said, assuming you got the virus from your ex (a very, very high probability if you were having genital contact (condoms do not prevent the spread of HPV well), then you could also bring it into any future relationship. It should be noted that the majority of the high risk strains that do cause cancer will go away on their own with time (usually before causing cancer), but you can spread them up to that time.
The vaccine can't do anything for someone who already has a strain of the virus (other than vaccinate against strains that person does not have).
It's probably wise for all women to have routine pap smears done every two years or so, especially with HPV exposure.
As well as many cancers of the vulva/vagina, penis, anus, tonsil, and conjunctiva. (all of which are greatly increased in the HIV+ population that have HPV)
Smoking also acts synergistically with HPV and women who have HPV and smoke, are at the very highest risk for developing cervical cancer. It is thought that smoking interferes with local epithelial immunity againsst the HPV virus. There is also some evidence that oral sex (thank you president Clinton) can spread the virus.