Why would people prefer to engage with Facebook instead of any other social network?

its all about presenting in a certain manner...
user friendly..

Again, the simplest answer is that its the most common social media platform out there.
As per the statistics from Dec 31, 2012 - Facebook had • 1.06 billion monthly active users (MAU) as of December 31, 2012 • 618 million daily active users (DAU) for December 2012 • 680 million mobile MAUs as of December 31 • Average time spent per Facebook visit: 20 minutes For more facebook stats, check out http://expandedramblings.com/index.php/by-the-numbers-17-amazing-facebook-stats/ There is no social network as big as the Facebook out there currently and no brand would want to lose out on engaging their target audience on this extremely popular, user-friendly medium.
Every marketer wants to reach out to the potential customer in the best possible way without being intrusive.
As Facebook has such a huge number of users who spend a considerable amount of time(much higher than other social networks) on it, why wouldn't anyone want to utilize that? Facebook has been able to engage its users regularly by bringing about interesting changes making it easier for the user as well as the marketer.

@Syed: Wow… That’s a pretty tough question my friend.
Well at the moment I cannot think of any ideas for a website to beat Facebook! But maybe the following below could be nice if they were added to Facebook itself: 1.
To have another different types of users (Normal User and a Corporate/Company user) where company users can interact and communicate using their own module for business deals.
2.
A customer support module within a fan page (Video/Audio) 3.
Customized pages where you can customize the look and feel, design and layout of your personal page 4.
Live event broadcasting for event pages 5.
Connecting your personal website/blog to your personal account 6.
Search for previous comments and activities (For example if you want to “Search” for an activity or a status update you did 3 years back instead of using the timeline manually to find it) Atleast I gave it a try! I hope I impressed you! *sigh*

Yes facebook stands ahead to follow with social network.

I guess the reason people and brands engage on Facebook is because it gives you the ability to engage in different ways (by providing an image along with a caption, or by a video with providing external links).
Facebook is more visualized, which means you can share updates providing images and videos and people can engage and share easily by one click.
Facebook uses AJAX platform in which it is light and compatible with all browsers and accessible from any device or mobile.
Last but not least, it is the largest traffic generating website, so it's definitely the place where all brands and people want to engage.

try to survey how many of your friends registered with other social network and you will discover that 95% of your contacts don't have any other network usage even if they have registered on other networks.
Maktoob Yahoo was the largest social network in the Middle East, they have been losing audience to Facebook on daily bases...
its all about demand and supply, the method of marketing, follow me on Facebook :-)

Because Facebook satisfy their needs and desires more than other social networking sites

Yes George, That's exactly my question as what type of social networking "website" could be used to be better than Facebook? I mean let suppose we have to create a Best Social Networking Website and we need to engage users more then the Facebook that what qualities or perfection requires on that newly developed Social Networking Website.

People prefer Facebook because it's easy to use and easy to understand.
Facebook is one of the largest traffic generating website in the world.
It's far reaching and very friendly for content sharing as it has pages and groups where you can promote what ever you want.
One more thing, you can control who has access to all parts of your profile. 
Privacy on facebook is much more customizable than any other social network.
However, I do prefer Twitter and Instagram!

George, excellent response to my question but friend, I need to ask you 1 more thing, as few days before, I was doing a survey for 1 of the new establishing mode based Social Network, where they asked me the same question which I am going to ask you now that can you describe in 5 points as to what Users Wants In Social Networking Website instead of Facebook? Have a nice day.
Syed Waqas Saghir Internet Marketing Expert, SEO Consultant, Social Media Evangelist.

Because Facebook offers a lot of free services It gives us all kinds of communication