The term reboot, in media dealing with serial fiction, means to discard much or even all previous continuity in the series and start anew with fresh ideas.
(reboot is pretty much synonymous with remake)
I haven't played very many reboots but Metroid: Zero Mission was good. The original Metroid was too homogeneous, everything looked too similar and hidden items and passageways were not apparent at all. Zero Mission made technical improvements on everything.
But my favorite, without a doubt - Bionic Commando: Rearmed. They took a great NES game and made it amazing. Developers should take note, THAT is how you do a remake. Keeps the spirit of the original yet improves upon it in so many ways.
I think you mean... http://en.wikipedia.org/wiki/Reboot_(fiction)
MK9 wasn't done right. The story was made even worse.
Final Fight Streetwise wasn't done right because they put zombies in the game and had poor dialogue.
DMC wasn't done right because it made the same mistakes as Final Fight Streetwise (dialogue). The original DMC wasn't all that great either. Story was boring and so was this one. The anime was even boring as heck.
Square did a good job of remaking Tomb Raider, True Crime, and Deus Ex.