Lots of games are being updated to incorporate features offered by the Google Play Games service, but it's still difficult to tell what's using what. For example, Modern Combat 4 is using Google Play based achievements and leaderboards, but they're using a proprietary multiplayer gameplay service.
Google has added unique badges that tell you exactly what games are using what features. Take a look at the screenshots below and you'll see badges for leaderboards, achievements and more. Of course, the leaderboards and achievements are the two most common features you'll find at the moment. There are also a few scattered badges for realtime multiplayer support. I haven't come across any games that support cloud saves yet, but when I see a title using the related badge I'll update this post accordingly.
Unfortunately, the badges haven't rolled out to every single title in the Google Play store offering Games support. Some of the apps even have conflicting app descriptions, for example the paid version of World of Goo displays the badges, while the free version page has none. It's probably going to take some time for Google to implement the badges for the entire Google Play storefront.
Of course, you'll need to have the latest version of the Play store to see the badges so keep that in mind.
As for the in-game Google Play Games menus, they look remarkably similar to the Google Play store design. That's to be expected really. Unlocking an achievement will share the milestone to an attached Google+ account, but this functionality can be turned off if you don't want everyone to know you're playing games at work.
Personally, the games I've tried include World of Goo, Modern Combat 4, Super Stickman Golf 2 and more. The new achievement system really just gives us another reason to play mobile games all the time.
It will be interesting to see how many games implement these new features and how many choose to ignore them. It's possible that achievement and leaderboards will become something of a rarity for Android games if developers decide not to offer support. Are there any games you would like to see these features come to? I for one would love to see support offered for Minecraft: Pocket Edition.