This incomplete list of best Free Android games is basically just going to be built up over time, if you have any games that need adding then leave a comment and I'll get on to trying them. Hopefully this list will slowly grow and we'll get a brilliant and deep collection of incredibly addictive and solid games. As a result of this list games will no longer be added to the list of Best Free Android Apps which will be left solely to Apps.
Alchemy
Alchemy is like so many amazing games in that the concept is simple. With Alchemy you add elements to make more elements in a simple game of logic that gets progressively more and more complex. Although the game can get boring and overly complicated after a while it's incredibly fun to begin with and one of the most popular games on the operating system.

Angry Birds series (including the original Angry Birds, Angry Birds Seasons and Angry Birds Rio)
The Angry Birds series is the standard bearer for mobile gaming and on the Android operating system. Although the original can seem clumsy at times the “Rio” edition which is the newest, is very smooth and brilliant. All three games are addictive and time consuming though you can easily enough pick it up just to fill a short break in the day.

Bomb Toss
Although very similar to Paper Toss (more about this one below) it's a much better game with more depth and has built on the same premise well. In Bomb Toss you throw bombs at on coming monsters to try and kill them before they get you. The game gets very difficult, very fun and frantic which is what makes it so much better than Paper Toss.

Bubble Blast II
Like so many games on the Android it's such a simple game that has an addictive quality. The game is about setting off chain reactions of bubbles to pop other bubbles and clear the screen. Although the game does get difficult it's one that is incredibly fun and worth downloading and picking up and playing when you've got 5 minutes.

Bubble Pop
A very attractive take on the Bust-a-Move games with a huge amount of levels, a beautiful look and very nice calming background music. If you can only have 1 Bust-a-Move clone pick this one (and whilst some others, such as Shoot Bubble are excellent, this one is just better) as it just has the prettier package. Although the game does have a slight twist on the well known concept it's the same game at heart.

Jewels (Jewels and Jewels Deluxe)
These are both Bejewelled clones so you know what you're getting with them though they are both ultimately, incredibly addictive and fun. Although the game isn't pushing the boundaries of what is possible on the Android phones they are addictive and they work wonderfully well with the touch screen ability of the phones.

Mathgame
If you like to be frustrated, tested and forced to tear your hair out whilst learning Mathgame is perfect for you. Eddie Hsu has created a game that is addictive, frustrating, simple and a learning tool all rolled into one. The game lives up to it's name and is a maths game in which you need to click on the onscreen numbers and functions to make an equation, sounds simple but is frustratingly difficult. If you liked Brain Training you will love this.

Math maniac
Another maths based game though one with a slightly better "package". Rather than creating equations (as you do in Mathgame) you need to select numbers to make a total as shown in the bottom corner. Again this a frantic game that is frustrating but yet addictive, educational and will not only test you but will also keep you coming back for more. Download it for kids then play it your folks, you will not be diasspointed.

Mouse Trap
Mouse Trap is one of a high number of games where you move blocks to to allow something (in this case a mouse) to get from one place to another. Although there is a lot of similar type of games this one is one of the deepest and most responsive. This will be a long time wasting game and one of the true pick up and play Android games.

Paper Toss
Simply this is about tossing paper into a bin. You use the touch screen to guide the balls of paper and try to gauge the power and angle (with wind being an added foe) to throw the paper into the bin. Although it's not as much fun as doing the same in the office it's much less messy.

Paradise Island
For you people who like to create your own farm and look after it this is the free Android game for you. You look after an island and need to build buildings to earn more money and buy more space and buildings. On the whole it's like like a Sim-City “lite” and whilst not very complex it is very playable and very addictive.

Pumpkins v Monsters
This is another frantic game though one that adds strategy to quick thoughts. To play Pumpkins v Monsters you need to put 3 Pumpkins of the same colour together then throw them at the oncoming monsters. The game is incredibly fun and one that gets progressively harder as you add tougher enemies and more colours of pumpkins.

Replica Island
As far as platform games on the Android go this is the best at the moment. You play as the little green Android icon that has been the operating systems mascot and go through a huge number of levels with clever controls and gloriously sharp graphics. The game features relatively poor sound effects but it is incredibly playable and the style is very "early 90's", a classic 2-D platform game if you will.

Shoot Bubble (Shoot Bubble and Shoot Bubble Deluxe)
For those of you who remember the "Bust-a-Move" games, this is going to be very familiar as it is, for all intents and purposes a clone. Shoot bubbles from the bottom of the screen to the top and try to connect 3 of the same colour to take them away. The game is incredibly addictive, very easy to play and the sort of classic game that we all feel comfortable playing. Whilst I prefer Bubble Pop (read above) these are worth downloading just for that bit more variation.

Tank Hero
Whilst Tank Hero isn't the prettiest face on the Android market it's the face of a game that is happy to go to war and blow up anything in it's way. The game features smart controls, a nice layout and a very addictive gameplay style that really is full with 80 levels of both campaign and survival mode as well as time trail. This one will have you occupied for quite some time.

Tetriss
The classic Tetris game that is one of the immortal games has been replicated for the Android system. Despite being addictive this version does have some tricky controls that do seem to take away slightly from the fun of the original Tetris. For now it's the best Tetris clone on the Android market (funnily a Bada one that I played on the Samsung Wave was better) and whilst it's still good, it's equally as frustrating as it is fun.

The King of OX
Another maths title which is again frustratingly addictive. This time you are "marking" the equations by clicking either an "O" if the answer is correct or "X" if the answer is wrong. You are racing against the clock to try and mark as many correct as possible and with the national and international leaderboards you will find yourself coming back to play it over and over.