With Metroid Prime, Gamecube finally reached its full potential as a video game system. At the time of the game's release, the console was in a bit of a drought. Some people had been disappointed in the Gamecube versions of other classic Nintendo franchises like Mario, and there was a lot of skepticism about Metroid Prime from critics and fans alike.
The general fact that it was being made by Retro Studios, an untested western development house, enhanced that skepticism. When news of a troubled development process leaked, things looked very grim. What fans didn't realize was that Nintendo's genius game designer, Shigeru Miyamoto, who created Mario and Zelda, was taking a special interest in Metroid Prime. Some of his suggestions helped make the game into a classic, including the first person viewpoint.
At the time when Miyamoto injected himself into the process, the game wasn't working out very well. Retro was making a third person 3D action game, and apparently it wasn't feeling like a Metroid game. According to reports, Miyamoto came in and started changing personnel, firing people who were ineffective, and promoting more successful workers. Then he hired a bunch of new people, and oversaw the initial re-design of the game.
Gamecube fans were terrified when they found out Metroid Prime would be a first person shooter, but Nintendo continually insisted that it was a first person adventure game, not a shooter. Fans had already been concerned about 3D graphics, and many would have preferred a 2.5D approach, with Super Metroid SNES style game play.
When it finally released, Metroid Prime Gamecube worked out much better than anybody expected. For one thing, it really wasn't a traditional first person shooter. The game used a lock-on mechanic, which made the gun-play much more like the sword fighting in a 3d Zelda game, and less like aiming in Halo. Secondly, it was absolutely a traditional Metroid game in every way, with open ended exploration of an alien environment, and a true sense of isolation. The designers implemented several cool features, including special visors designed to help the player explore more efficiently. The story was told through the scan visor, which let the player analyze objects in the environment and read computer logs.
The Metroid Prime boss fights and level design were both similar to classic Metroid games, and they even managed to implement several fun platforming challenges, despite the first person view. The art design was exquisite, and everything about the game was incredibly polished. Critics were blown away, and most major video game sites scored the game very high.
Some Metroid purists were unhappy with the game, and they felt that the series had drifted too far from its roots with Metroid Prime. Gamecube was the first system with true 3D graphics to ever host a Metroid game, and some fans were unwilling to give up the 2D aspects of the original game play. They felt that 3d slowed down the play experience in Metroid Prime Gamecube, preferring the rapid movement and play style of the classic series. But generally, these viewpoints were rare, and most people enjoyed the experience of looking through Samus Aran's eyes while exploring.
Now that a few years have passed, it's pretty clear that Metroid Prime Gamecube was probably the best overall game on the system. There are a few other possible choices, including The Legend of Zelda: Windwaker, but in this case it's pretty clear that Metroid Prime was the most interesting and polished game released for the gamecube. One possible exception would be Legend of Zelda Twilight Princess, but it was actually more fun on the Wii, and it's definitely questionable whether or not that game is truly better than Metroid Prime anyway.