Some game series are strong enough in setting, storyline, and theme that they work well in multiple genres. Super Mario RPG comes to mind as a good genre change, though it isn't exactly 100% faithful to its source material. Perhaps the best transition has been The House of the Dead 2, which went from light-gun shooter to typing game to English trainer. Postman, of the blog Shoot the Core (apparently a Gradius fan to begin with), has reimagined Konami's legendary shooter in a much slower-paced gametype: an Infocom-style text adventure.
The results, predictably, are awesome. It's Gradius! Even as a completely different, vaguely nonsensical game, it's great.