Since I'm only 21 and my family never travels, I haven't really had the opportunity to try a religious pilgrimage.
However, swimming in Lake Victoria sure felt like one! It's the worst I've ever felt and the best I've ever felt - the worst b/c I was so sick for two weeks from whatever I caught and completely exhausted from the heat and lack of edible foods, but the best b/c the water was 80 degrees, the sun was shining, the beach was clean, kids were playing on their way home from school, local people were fishing with their nets...it never felt so good to be so far from home.
This isn't really a pilgrimage, but a few months ago, our air compressor in our computer shop at work broke. Another collegue was showing me the room where the air pipe originates, so we could check for a leak. The room was upstairs in the college library, where they store a bunch of old cool books. We were kinda joking around until we got to the room and the guy said "don't touch ANYTHING". At that time I didn't know what was in the room, but it was full of old Bibles. I stopped right in front of one from the mid-1500s. It was probably one of John Calvin's own Bibles, since our college is named after him and we're from a Calvinist denomination. I just stood there frozen in front of that book; I was afraid to breathe on it. It was so creepy and cool at the same time.