Two of my very favorite games have finally come out for Android. I found them originally when I got an iPhone and I've missed them.
1) Scrabble -- I know lots of people don't like Scrabble but I love to play. I love the challenge of figuring out where to put words. I love figuring out how to place them for maximum points. The only thing I don't like about Scrabble for Android is that it doesn't have a play offline feature like the original for iPhone did. This is perhaps because its a free version. They aren't offering a paid version yet. I learned lots of word placement and unique words by playing the computer.
Remember Speedo Man? On another occasion when he wouldn't leave me alone I was playing Scrabble on my phone in the hot tub. Speedo Man was just as clueless then as the previous time.
2) Doodle Bowl -- This is a fun game that tries to replicate real bowling on your phone. You touch the ball to pick it up and then flick it down the lane. If you've screwed up and react fast enough, a quick swipe across the screen will attempt to put a spin on the ball. The original alley is quite literally a drawing. The background is notebook paper and your ball and pins are doodles. When you toss the ball it crashes through the paper at the end of the lane. As you play games you earn credits and can unlock more alleys. There's a fire alley, a "back" alley (get it? hahaha), and a space alley, for example. There's even an alley under the sea where your pins look like they're made of air (much like Bubble Buddy from SpongeBob SquarePants).
I also enjoy playing Plants vs Zombies on my phone. It requires actual thinking to complete the game versus beating the ever popular Angry Birds. I have Angry Birds in all its incarnations and I have to say that I don't really like it. It is difficult, in my opinion, to learn from your mistakes and position the bird just slightly from where it was before to reach your goal.
My all time favorite mindless phone game is Tetris. I have had it on my last five phones. The latest version from EA is by far the best, in my opinion. It is a great stress reliever and I enjoy it because it requires little brain power. Its just flick, flick, double tap, slide.
What do you enjoy playing on your phone?