My first mainstream recognition of the grid design was on Pinterest. Social news feeds have always been in a streamlined fashion such as Twitter or Tumblr. Nowadays even many Facebook pages scatter timeline updates to appear like a grid.
This isn’t something you can force into any old website. There needs to be a purpose, the user experience always comes first. In situations using thumbnail images or text updates the grid layout condenses everything into an easy-to-read format. Everything is skimmable yet still coherent and it doesn’t require much space on the page.
Open source JS libraries such as Masonry can do a lot of the hard work for you. Not many websites utilize this feature but the ones that do are often quite pleasant on the eyes.