Most likely the game would be much less popular if it did not have an online mode.
Several of them are popular. A few of them are the Star Wars Xbox 360 Kinect, Star Wars The Old Republic, and the multiplayer online game, Knights of the Old Republic
If they were popular Xbox Orignal games then most likely you can play them on your xbox 360.
The Halo games have long been the most popular game for the 360. Halo 3 is currently at the top.
Roblox
Xbox live was on the original Xbox, meaning that there are several games which you can play online. Halo was the most popular game on the xbox. You can still play these games but noone will be playing them as the Xbox 360 has more and latest released games. Also, you cannot play Xbox 360 on the original Xbox, FACT!
Halo 3 by far, then COD WaW
The most popular games on the web is RuneScape and Club Penguin.
Roblox
go to (in the question box) "What is the most popular online adventure game?"
I, myself, do not play it, but World of Warcraft must be the most popular on the internet.
The most popular war game online is World of Warcraft. World of Warcraft has been played extensively by many people since 2004 and continues to be one of the most popular games to date.