Java ME mobile phones
Before the 2.5 generation of cell phones mobile games came pre-installed with a device. If you wanted a new game you had to buy a new phone. Everything changed when mobile phones began to modernize. The introduction of Java ME, GPRS internet services and color display changed games. They became more advanced and could be downloaded on a phone via the mobile operator's network. Camera phones and EDGE internet services (called sometimes 2.75G) were another significant step in the evolution of mobile games. Their storage and graphic capabilities allowed production of higher quality games. Unfortunately Java games were still inferior in comparison with handheld console games due to the lack of processing power of the phones. Also there are a shitload of titles based on a movie licenses or dumbed down versions of console games produced only for quick cash. Because of that unlike in Japan mobile phone games never broke through in the US and Europe until the arrival of Apple and Android smartphones.
- For emulators, see J2ME emulators and Emulators on J2ME.

If you want to emulate Java games on your PC probably the best way will be KEmulator Lite In a case of issues with running it check Java Runtime Environment version installed on your PC. It should be ok with JRE 6 Update 33 but in a case of troubles try with other versions. There should be also Java ME emulators for iPhone/iPad and Android. If you want to play these games at your standard Java phone you can load them easily via Bluetooth, memory card or through WAP Games usually came in few different versions made for different phone models. They don't have to match exactly. A lot of games will run on different phone model that they were intended to. More important can be screen resolution or .jar file size so running them could be trial of error.
Java games are very easy to translate, there are a lot of tools for that on the internet. Also Japanese mobile games can't be emulated or played on non Japanese phones because of their distribution structure that resembles cloud gaming.