Are private servers for currently-running massive multiplayer games illegal? It depends a lot on your interpretation of the Digital Millennium Copyright Act. Blizzard has won battles in court against "emulated servers", but it seems that other publishers have no problem with fans running their own private servers as long as they are for free.
The game that has one of the larger followings of private servers is Lineage II. It has had decent success here in the US, but it's much more popular in the developers' native country of South Korea and in other countries in Asia. With an anime style and a brutal levelling curve (where months of play, even at eight hours per day, won't even put you close to the maximum attainable level), it satisfies both the tastes and need for challenge that Korean players have. But in the US, many players found the game's incredibly long "grind" just way too much to swallow - and those who love PvP aren't happy with the fact that even PvP deaths in Lineage II result in a considerable XP loss (even if someone much higher level than you kills you in a single hit).
A Massively Multiplayer Online Game (MMOG or MMO) is a computer game which is
capable of supporting hundreds or thousands of players simultaneously, and is
played on the Internet. Typically, this type of game is played in a giant
persistent world. MMOs can enable players to compete with and against each other
on a grand scale, and sometimes to interact meaningfully with people around the
world. Most MMOs require players to invest large amounts of their time into the
game. Many MMOs can be found free on the Internet.