Produced in the mid-2000s by Alderac Entertainment, the "Stargate SG1" roleplaying game used a modified version of the award-winning "Spycraft" rule set. It allowed players to take on the role of Stargate Command Officers and several follow up supplements were released expanding on the rules, providing additional information from the TV show and providing Games Masters' with original settings. Whilst it's no longer in production, pdf format files of the original rulebook and "First Steps," a supplement detailing new locations, are available from websites such as RPGNow and DriveThruRPG.
Whilst the Alderac Entertainment edition was the first "Stargate" RPG to be released it wasn't the first to be written. In 1998, West End Games contracted game designer John Tynes to produce a "Stargate SG1" roleplaying game. Tynes used West End Games' own D6-based system and produced 30,000 words of game material before the company hit financial difficulties and the project was canceled. Tynes subsequently put the material up on his own website for free.
Play by email games are games where players communicate both in and out of character via an email list or digest. PBEM games tend to have specific formats they want players to post in. Be sure to research this, and make sure the game is still active and welcomes newcomers before applying. "Stargate: Skywatch" is an excellent example of a pbem, with six active teams of player characters.
The "Stargate" universe is also a good fit for live action roleplaying, with "LARPers" able to find most of their costumes at army surplus stores and the franchise's frequently forested or grassland locations easy to replicate. The most successful "Stargate" LARP group to date operates in England, and their website provides a wealth of information on their game world, as well as the rules set they use and ideas for anyone looking to set up their own group.