MeBoy is a Gameboy emulator for mobile phones (which means you can use it to play Gameboy games on a mobile phone). It works on phones with support for Java Micro Edition, specifically MIDP 2.0. Your phone manufacturer's web site can tell you if this includes your phone.
MeBoy supports both Gameboy and Gameboy Color games, and with version 2.0 you can even play your games with sound!
With MeBoy you can also save your progress at any time, whether the game itself supports saving or not. Any number of saved games can be stored concurrenly (only limited by your phone's available storage space). Since version 2.0, you can share your saved games with your friends via Bluetooth.
I started working on MeBoy in 2005 after I wondered why there was no way of running Gameboy games on my (at that time) new and shiny mobile phone. Determined to rectify the situation, I started work on MeBoy by porting JavaBoy to J2ME (JavaBoy is a Java-based Gameboy emulator for PCs, written by Neil Millstone). The direct port could only emulate a single frame per second! Lots and lots of optimization later, MeBoy was ready for release. Luckily, it is also getting faster every time a new phone model is released!