I've been looking around and I can't seem to find an automatic (i.e. buzz- or Twitter-like) way to follow users inside Stack Exchange. Why haven't the developers added such a feature? It could help beginner users follow other beginners with the same interests. We would be able to learn from each others' questions and pitfalls. Also, it would reduce double posting.
You can always follow a user's RSS Feed. You will find the icon on every user page.
It is possible to browse all posts by a specific user; just use the activity tab and filter by posts:
There is an extension for Google Chrome and Firefox called FriendOverflow to follow your friends: