[AT&T Samsung Galaxy Note I717] littlewierdo:
Not in any particular order:

Robo Defense (Paid version). While this is a standard tower defense game, it has nearly unlimited playability. Whether you complete a map or not, your final score is added to a total where you can purchase permanent upgrades for future map plays (for example, making all 'machine gun' towers do additional damage or flame towers burn enemies for a longer period of time, any upgrades purchased are permanent and carried over for future play thrus.). With over 10,000 maps to play and 100 difficulty levels for each map (100 waves for each map regardless of difficulty), it always feels like there is progression. I have not completed or maxed out any upgrades yet, this one has the ability to keep you entertained for a long time.

Myth Defense. Another Tower Defense game with a different permanent upgrade mechanic to Robo Defense. The key is, I like persistence and a tower defense game that doesnt allow me to feel like there is some sort of progress other than unlocking a new map to play doesnt really interest me. Myth Defense has an upgrade mechanic that allows me to feel like I am getting more and more powerful. There are two or three additional map addons available on the market as well (they are paid $1 a piece).

Gem Miner Dig Deeper & Gem Miner 2 (two different games, both paid). A rather simple, laid back game where the objective is to dig around in a mine collecting gems/metals to sell (to upgrade equipment to allow for deeper digging each return to the mine) and blueprints for the ability to get upgraded equipment made available (things like a drill rather than a pickaxe for faster digging at the cost of fuel expenses to run the drill), again, this one is just fun and laid back. I like the ability to just play casually and customize the mine how I want it laid out. There also is some 'shorter' objective based modes based on completing tasks such as collecting a certain amount of gems/metals within a set amount of time, digging to a certain depth, etc. Again, these are two different games so for those that only have the first one and didnt realize there was a sequel just recently released, now you know.

Glyder 2. Casual flying around differently themed maps to collect jewels cleverly scattered thru each map. Upgrades are available as you collect more and more gems, unlocking new maps to play and new equipment. You do not need to collect everything in a map to progress and its a good thing because some of the gems are VERY cleverly hidden. It is a 3d perspective using the phone tilt to control the character.

X-Plane. Like flying? Dont want to worry about being shot down? Just want to cruise the skies? Here is the game. Like MS Flight Sim and has lots of options to tweak. Only negative is, there are ALOT of in-game purchases including new planes and new islands.

Shredder Chess and Mobalia Chess. If you like chess or want to learn the game, here are the two premier apps. I have purchased both and like them each for their own different reasons.

Jenga. A simple physics based game, remove a block from the middle of the tower and put it at the top of the tower. Very pretty looking game although, it is just Jenga, nothing more, nothing less.

Battleheart. A relatively simple action rpg well designed for touch. Theres not much of a story but plenty of lewts and levels to gain. I think this is a really shining example of how to write a game for touch without using virtual pads on the display.

Anything that looks interesting by Kairasoft (just search the market for Kairasoft or Game Dev Story). Everything they make is awesome, although, in a sense, once youve played a couple of their games, the only thing that changes is the theme, the treadmill is much the same. But I still like their games, my favorite still being Game Dev Story.