I've heard anecdotal evidence of women who begin taking the pill while still in puberty, then stop taking it in their twenties and find that they've stopped ovulating permanently. A serious consideration, to be sure, when considering your birth control options.
Now, all the research I can find online says this won't happen, and I Am Not A Doctor myself. Doctors will tell you freely that it's not unusual for a woman's period to take up to six months to restart after getting off the pill. According to one source, it can take up to two years to restart in a small percentage of women. It's possible that some of the women in that last group are the ones seeking infertility treatment, since "infertility" is defined as being unable to conceive after trying for twelve months.
In addition, it seems some teenagers are prescribed birth control pills because of irregular periods, which also can be tied to infertility. For those women, going off the pill will cause the irregular periods to return, but not their fertility.