In general, Judaism does not promote or approve of lifelong chastity. Our tradition does not teach that sex is inherently sinful-- at worst, only outside the context of a legal and monogamous marriage would it be sinful; at best, only in the contexts of specifically prohibited relations or rape would it be sinful. But if nothing else, chastity inhibits fulfilling the commandment to procreate, and the tradition deems that commandment incumbent upon everyone. And, in general, the Jewish tradition is not excessively ascetic.
As for premarital chastity, it depends on who you ask.
If you ask most Orthodox Jews, they will say that it is important and a matter of Jewish law that people remain chaste prior to marriage.
If you ask most non-Orthodox Jews, and a few Modern Orthodox Jews, they will say that Jewish law does not necessarily stipulate that people remain chaste before marriage. Some will say that it might be better, more advisable to remain chaste before marriage. Some will say that while chastity is unecessary, one should be minimal in one's premarital sexual exploits. And some will say that chastity is counterproductive, and so long as one's sexual relations are safe and consensual, there are no limits to sexual relations prior to marriage.