If you are lucky and if he/she is the right one.. then the newness just transforms into something deeper, more close and more wonderful... The excitement need not go away and sometimes newness can mean a slight awkwardness so to be honest, getting past that stage can be a fabulous thing :)
That all depends on the persons in the relationship. Some wear off faster than others. Sometimes, the the newness stays there forever because you love them so much that everyday becomes an adventure.