A game which can be played on mobile phones ia called as mobilegames other devices also comes in same category like , smartphone, PDA, handheld computer.
Categories which are excluded from this calsiification is of latest gaming system like  PS3 or PlayStation3 from Sony, Xbox 360 From Microsoft, Nintendo Wii from Nintendo.
Snake was the first mobilegame, The game  snake was preinstalled onto selected Nokia mobile phones. The game is so old but still popular new variants are available in the market some games like tetris is the latest variant and popular among many game players.
Internet is not the problem to play mobilegames on mobile phones these mobile games are non networked applications, that simply use the device platform to run the game software.
But now in 2010 mobilegames industry has changed a lot now you can play online mobile games, any type of mobile phone plenty of games are available on the net, searches like Free nokia mobilegames, free samsung mobilegames and of any device you can find out thousands of website allowingy you to play free online mobilegames.
Mobilegames can be easily downloaded from the internet just with the help of google search find you top mobilegames and download on your Computer or PC and from there simply download the mobilegame onto your mobile phone with the help of  infrared connection, Bluetooth, or memory card, data cable anything, but  a word of caution download only those mobilegames which can be played on your mobile phones, before downloading the games online check is the mobile game is compatable for your mobilegame or not.
This will save your precious time and can get Free mobilegames for your mobile phone for free in 2010.