1. 1 year head start: Historically, releasing a capable console before the competition (Nes, Genesis, PS1, PS2) is going to result in a successful console. As long as it can do pretty much what the competition will do.
2. "Affordable" Price: It launched for $300-$400. Not too bad. It offered other features for a fee (Wi-Fi, etc.), but the entry fee wasn't too much to swallow
3. Gears of War: When the competition launched, this game launched, too. It was graphically ahead of anything anybody else was showing.
4. Media Darling: The 360 could do no wrong in the eyes of the video game press. They were too busy hating on the competition.
5. Xbox Live: If you have friends online, this is the most fun you can have with a video console. It really is an online community.
6. Third party support: It seems that every company embraced the console. As a result, it recieved a far more diverse library of games than MS's previous console. Even franchises that historically never came to the Xbox brand came along to make money.
7. Advertisements: As a relative newcomer, Microsoft proved to be remarkably savvy when it came to marketing their product as "cool" and "must have". Perception is everything.
8. Hardware Reliability: Wait. What? Yes. It's true. In the past, Microsoft's Xbox was hailed as an amazingly well designed machine. Compared to the competition, it rarely broke down. Many were unhappy with their console (from the competition) during the 5th and 6th gen. They broke down early and often. With all of the same games (and a few exclusives) on the Xbox 360, for a lower price, AND a reputation for better reliability? Little did we know.......
9. Brand Loyalty (Halo): The franchise was incredibly popular in the 6th gen. While fans of other consoles were jumping ship and trying out the Xbox 360, fans of Halo were loyal to the core. The 360 was the only place to "Finish the Fight" and it seems that they all came along. Halo had a large fanbase on the Xbox. Even though the Xbox didn't sell as much as the competition last gen, the percentage of owners that liked the franchise was incredible.
10. Dumb luck: Issues with the other consoles (graphics, game libraries, ease of programming, pricing, functionality) were beyond Microsoft's control. A lot of things Microsoft did right, other consoles inexplicably did wrong (initially). Once again, a console succeeded by simply doing key things right that other companies didn't.
Good PR guys didn't hurt things, either.
