The website of Perpetual Entertainment offers a press release announcing that this company will be developing a Star Trek MMORPG. The game isn't coming out any time soon though, with a public beta test expected late 2006 and the launch of the game not happening until early 2007.

The game will deliver action, adventure and combat mechanics unique to persistent world games. Its design includes a rich array of solo and multiplayer missions set in space, on planets and in starbases throughout the universe. At launch, it will take place during the 24th century timeline in the series with other aspects of the Star Trek universe to be interwoven and added through expansions.
"Players will encounter characters, places, and situations from their favorite Star Trek movies and television series; will explore incredible new worlds; and will cooperate with or battle friendly and hostile races throughout the game," said Chris McKibbin, President of Perpetual Entertainment.

There's a FAQ on the game at the official Star Trek website. Update: PC.IGN has a developer Q&A.