I've heard many people talk of an exotic vendor named Xur who only comes on the weekends, but I couldn't find him anywhere in the tower, and he wasn't on the map either this weekend. I was wondering if someone could just clear this up. Also, does he always have the same stuff, is it random, or is it a cycle of some sort.
Those people are indeed correct in saying that Xur can be found in the tower on the weekends. He is present at the tower between 9 am Friday and 9 am Sunday GMT (apply your local time difference to this). As to his location, it is changed every week, he can spawn in either of the three wings of the tower but a quick search should find you in his presence. The loot that Xur sells is also randomized each week and you should be able to find out his inventory for the week from a number of websites, I use this one here. Start saving those strange coins!