I'm a Nokia user and every now and then I feel like playing something with my phone. Here's a little list of games of enjoyable games, in no particular order. They should work with other models than Nokia as well as they are made with Java.
Ukko's Escape. A free and addictive one thumb game where your mission is to keep jumping upwards to make Ukko happy. Ukko's happiness decreases if he falls or does not jump and when he's out of happiness the game ends -- unless you managed to actually jump all the way up, in which case you win. The levels get increasingly harder and you can feel how you are making progress when you get further and further with each try. Ukko's Escape has even got a global highscore list at RumbleX and it seems that my record for the Hard difficulty level is still unbeaten. :)
Yet Another Tetris. Just what the title says, but this is the best free mobile implementation that I have come across. The arcade mode keeps the games short and hectic when extra rows are regularly added to the bottom of the screen. :)
Rollercoaster Revolution 99 Tracks. This is a commercial game but I once came across an offer and got it for free. In the game you control the speed of rollercoaster cars and try to collect smileys while avoiding crashing. As the game progresses you unlock new tracks, a couple of new car types and so-called awards, which are just cosmetic but nice anyway. 99 tracks do sometimes make it feel like the game was repeating itself, but if you like perfecting your accomplishments then this game might just be for you. There's also a free online version of the game available.
Tower Wars. I had actually forgotten about this free game, found it again when writing this post and ended up playing it for quite a while. Tower Wars is a tower defense game. In the game you place various kinds of gun turrets in front of forces of Chaos and either try to create a maze for them or to fill the edges of existing mazes with as effective cannon setups as possible. The graphics are good and there's a nice twist in that the game progresses through decades and millenniums: you start with rock-slinging huts and progress all the way to laser turrets and such. My online favorite of the genre is Desktop Tower Defense. :)