Pinterest's design exemplifies form following function. It's built to fill the most space possible with visual content, and is highly interactive allowing the site to hide all of its "extra" information like saving pins and personal boards behind a single click.
The New York Times need to communicate a ton of information; considering their task of displaying a range of articles on different topics, I think they've been successful at avoiding flooding their readers with too much information. First, they've been able to stick with the newspaper aesthetic while mainting a degree of whitespace. They also offer a choice of different articles to read across the screen horizontally, but rarely show more than 2 or 3 in a row at a time (unless there is a section specifically for that). I think this avoids a totally overhwelming experience for the reader while still communicating plenty of information. And of course, the topics tabs at the top of the page allow further filtering and organization of what is shown.
I like Function of Beauty's website for how they've centered around clear actionables. Most of the information on the website is provided based on what customers have come to the site for - for example, for haircare, there is one large button front and center on a page full of whitespace telling customers to take a hair quiz, and so on for skin, various products, and so forth. For a brand specializing in customization, they work to tailor their site to their customers' needs. They also have chosen and stuck with a pleasing color palette and have limited the amount of clutter across their site.