Google's Official Blog has announced the new Play Store version 4 which was leaked earlier on sites such as TechCrunch, and is now available for download. That's right, it's a rolling out product launch, so some users might not get the update for another few weeks. Fortunately, the .apk is available for download (links below).
The new Play Store feels faster, smoother, and in general more modern. The main screen isn't showing any content, rather just 5 boxes representing the categories (apps, games, movies, books, and magazines). From there, each box will take you to a different section, as you'd expect. Each section has it's own color scheme (the top bar, cost, and current tab indicator all change to the section color). Somewhat oddly, apps and games share the same (ugly) green color.
The UI acts very similarly to it used to, with the sub-sections (top paid/top free, top grossing etc) scrolling horizontally, and the categories on the left. The layout is cleaner, but gives less information. On my Nexus 4, I can see 5 full (and 1 title) apps per screen while I used to get 10+. This is mostly due to the fact that each app/movie/game/song/book takes the full width of the screen.
For further reading, here are links to Google's Official Blog, Tech Crunch's original 'leak' post, and the .apk download link, provided by DroidLife.