For many Orthodox Jews, the concept of not touching—known in Hebrew as Shomer Negiah, literally translated as "observant of the laws of touching"—is nothing new. The idea behind Shomer Negiah is that sex should be kept as something special that happens between a husband and a wife. Sex outside of marriage is a no-no. Anything that could possibly lead to sex outside of marriage is also a no-no. Think of it as an attempt to avoid any possible slippery slopes. No pun intended.
Orthodox Jews have varying views about how far the rules of not touching should go. Some Jews won't even take a seat on the subway next to someone of the opposite gender. Others will go as far as having oral sex, while still avoiding the "home run."
Personally, I don't think there's anything wrong with non-sexual contact, including hugging or dancing. Yet, when it comes to all that other stuff, I like to think I'm "selectively Shomer Negiah," which means I get a little more lax if the guy I'm with is really cute, but I definitely won't go "all the way," no matter how much I want to.
Depending on level of observance, when it comes to dating the rules of Shomer Negiah are either implicitly enforced or called into question. I've been on a first date where a less observant guy asked me if I was Shomer Negiah and wondered how "far" I was willing to go before marriage. Pretty rude, dude. Essentially, it's the Orthodox Jewish equivalent of being asked if I give blowjobs regularly. But shitty first dates comes with the territory when you're a single gal living in NYC.