It is very possible. My husband and I chose to not have sex until we were married for personal reasons (and we didn't). We were married three years ago (and we were in our 20s).
I think it was both easy and hard on each of us for different reasons. The easy part was that we simply "didn't have to worry about it." With sex out of the picture, we could focus on the friendship part of our relationship and we became extremely good friends. (In fact, even after we were married, sex seemed to complicate things for quite some time).
Difficulties for him: I think he is more "wired" for sex than I am, so he "wanted" it more (though he was always a perfect gentleman).
Difficulties for me: I grew up in a culture where it was abnormal for people to not have sex before they were married. I was afraid that if I didn't "put out" (even though both he and I agreed that we wouldn't), that I would lose him. My problem was more phycological than physiological.
I know that some people choose to not kiss or even hold hands before they are married and that is their choice (though I personally think that could be taking things to another extreme). We personally had no problems with that. We made boundaries and we kept to those boundaries. We even lived in the same apartment before we were married (and still didn't have sex). It is very possible.