Short answer: No, people on Facebook won't know if you look at their profiles, Timelines, posts or comments. Moreover, Facebook prevents apps from tracking profile visitors, so your anonymity as a viewer is guaranteed. That said, as soon as you interact with someone's profile, you lose that anonymity, so take care about what you click if you're trying to stay incognito.
Tracking Profile Visits
Facebook answers the question of viewer tracking bluntly: "Facebook doesn't let you track who views your profile or your posts." That means that when you open someone's profile, the person receives no notification -- there's not even a hit counter for tracking how many people visit a profile. Even third-party apps aren't allowed to track profile views, so if one claims to, Facebook asks that you report it.
Revealing Your Presence
Simply opening a profile page won't give away your presence, but Liking a post will. When you Like a post -- including a photo or link -- it leaves your name behind in the "People Who Like This" list, which anyone who can see the post can view. Having Liked a post doesn't necessarily mean that you've been lurking on the poster's profile page, since you could have come across the post somewhere else, but it's a strong indication that you visited. Similarly, commenting on a post or sharing it to your Timeline also leaves your name visible.
Facebook Page Insights
Unlike individual profiles, Facebook Pages for brands and organizations do track viewership data. Page owners still won't see your name unless you Like a Page or its content, but an analytics tool called Page Insights tracks demographics. Page owners can monitor their readers' age, gender, location and language. These statistics are compiled in bulk, however -- an owner can't identify you personally from this information.
