Negiah (Hebrew: נגיעה), literally "touch," is the concept in Halakha that forbids or restricts physical contact with a member of the opposite sex (except for one's spouse, children, grandchildren, parents, and grandparents).   A person who abides by this Halakha is colloquially described as a Shomer Negiah (one who is "observant of Negiah").
The laws of Negiah are typically followed by Orthodox Jews, with varying levels of observance. Some Orthodox Jews follow the laws so strictly, they take extreme measures to avoid even accidental contact, such as refusal to sit next to a member of the opposite sex on a bus, airplane, or other similar seating situation. Others are more lenient, only avoiding purposeful contact.
I have been wondering for years why so many Orthodox men are so uncomfortable shaking hands with me. Not that tons of them cross my path, here in New York they tend to stay within their own communities, and when I do see them they avoid eye contact with me and do not return my hellos. I understand, and don't take offense, but I have always been saddened that this entire segment of humanity is closed to me, especially since it's segment of a people with whom I identify, who practice a religion that I am joining.
A lot of Christians are exactly the same. And some Eastern faith followers as well. However I have never detected the animosity from Jews that seems to simmer beneath the surface of many religious men. It's just a nervousness, almost an apologetic shug, as they quickly move away, eyes downcast.
It also occurs to me that I'm a particularly disturbing sort of shicksa, since I wear pretty revealing clothing, flashy jewelry, makeup, high heels, I have this bright red hair that I wear like a crown, I have a BIG saucy personality... The one time an Orthodox man spoke to me, it was on a shabbat elevator at a hospital, and I was wearing a very modest dress, and had my hair in a braid down my back, and no makeup or jewelry. His name was Aaron, and seemed to be slightly flirting. I was amazed... and then my colleagues told me afterwards, "well, you're dressed like one of them!" Oh...
The one time I was able to meet, talk to, and believe it or not party with a small group of "frum" guys, it was a thrill for me. We sang hymns together, partly in hebrew, on the sidewalk, in 5-part harmony. I felt loved! And I remember that one of those men was married, and he was he one who most most uncomfortable with contact. The rest of them were single, and one even danced with me. I figured maybe they were less strict than they looked? Now I'm thinking... they were probably a bunch of guys misbehaving just for an evening. Like all normal people! It was harmless, and a lot of fun, and they made a wonderful impression on me. For them - that's a mitzvah.
Now that I'm married to my soul mate, I have calmed down considerably in regards to the opposite sex. I'll always be a flirt, but now I'm all talk. And even my talk isn't as bad as it used to be. I understand this is how I want to be, how I want to live my life, not only out of respect for my husband, but for myself, and the kind of life I want to live, the kind of person I want to be. I want to leave the wantonness, for the most part, behind me. I don't need it anymore. I want to see what's new in life. I like the new me. I feel stronger, more independent. And I do think, arrogantly perhaps, that G-d is pleased with me. Not that S/He was angry or disgusted or anything like that before... but I was a furious, raging adolescent, getting into trouble, and constantly running to G-d in tears, seeking solace. That's over now. And I think S/He is proud of me.
I am proud to be who I am. I'm excited to see who I am becoming. I've accepted who I was. And I love the idea that, in some way, I am all three at once.