There's a lot of open source games available for Android. Some are ports of open source computer games, others are just engines that let you play proprietary games from other systems on your smartphone, and of course there are games made specifically for Android that just happen to be open source. I thought I'd list the most interesting and fun ones I've been able to find.
Having the code available makes these games great for learning, though I like to look at example code from smaller games because it's easier to understand what's going on. My Libgdx example game is uber simplistic for that reason. Unlike that "game", the projects in this list are proper games that are actually designed to be fun to play. There are other FLOSS games out for Android, but these are the ones I had the most fun playing and the ones that I think are the most impressive.
8 - ScummVM - The ScummVM project lets you play classic graphical adventure games, like the early LucasArts point and click games, on modern systems. While ScummVM is open source most of the games it runs are proprietary, but at least two good ones are available for free: Beneath A Steel Sky and Flight of the Amazon Queen. The Android port is unfortunately a work in progress and it's not yet available on current Android versions above 1.5 or 1.6.
7 - Missile intercept - A classic missile command clone with appropriately retro graphics. This game adjusts to landscape or portrait mode. Good for quick play sessions. I haven't looked at the source, but this seems like it'd be a good game to learn from.
6 - OpenTyrian - This Android port of the desktop version of OpenTyrian is a lot of fun to play. Tyrian was released before I got my first PC, so I missed out on it back then. I was a little surprised when I found out people like Daniel Cook and Alexander Brandon had worked on that game. Daniel Cook runs LostGarden and Alexander Brandon worked on the music for Deus Ex and Mask of the Betrayer, two of my favorite games and soundtracks.
5 - Replica Island - I found it a bit tough to control precisely on a phone without a keyboard, but I played a few sessions of this game at a table using my Bluetooth mini keyboard. It's a fun take on a side-scrolling platformer, starring the little green Android mascot.
4 - Kwaak3 - Now here's a really interesting project. An Android port of the open source ioquake3 engine that lets you play all of Quake 3 Arena if you've got the data files sitting around. You can download the Quake 3 demo if you don't own the game already and run that. Needs a keyboard to play, but there was a touchscreen variant called Kwaak3 Arena or Quake3Droid floating around online.
3 - Frozen Bubble - This is an addictive game on the desktop, and it's every bit as addictive on my phone. Digital crack at it's finest. I've gotten a couple of relatives into it, one completed the whole game, even the really challenging later levels. Frozen Bubble is the perfect casual game.
2 - GemRB - Baldur's Gate 2 on your smartphone!!! I have no words to describe how awesome this is. I LOVE Baldur's Gate 2, and all the Infinity Engine games. I had first heard of GemRB around 2006 when I was looking into playing Baldur's Gate 1 in Linux using WINE, but at that time a lot of functionality was missing. Now it seems like you can more or less play through Baldur's Gate 1+2, although some things are still missing or broken. This is an immense project that will be the future of Baldur's Gate fandom. I can't tell you how cool it was for me to see the Baldur's Gate 2 main menu screen loaded on my Inspire 4G. This is motivating me to try and get a Bluetooth mouse working on my phone.
1 - The Ur-Quan Masters - Here's another proprietary game (Star Control 2) that was open-sourced and now has an Android port. I completed this game on my laptop some months back (right before playing Mass Effect 2, it made the planet exploration of ME2 look like crud in comparison) and then I found the Android port. This is a game that really stood the test of time. It's best played with a real keyboard. Just go play it if you haven't already, it's a lot of fun.