Or, does it matter?
I think the content of the website it's self is the biggest issue, personally. I mean.. when I'm searching for something on Google I'll go for key words that will hit what I'm interested in or needing. Usually my key words will bring up mixed results (.com, .net, .org, etc).
I use a .org website daily, and we've had well over 100,000 registered users there. I use FA almost every day, too, and I'm pretty sure we have over 100,000 people here as well.
So.. I don't think the ending letters have as much impact as the actual content. If you build something that will help a lot of people or interest them, people will visit regardless. If you treat people well, they will care about the site and come back.
It should be all about promotion and product or service as far as the popularity goes. Mr. Goodrich is right. If you are trying to choose a domain name you should consider what it is going to be used for to help in the popularity. For example, I use a .net address as I have an art site and a writing site that are non commercial so I avoided .com
They don't come much more popular than this:
..... or more influencial on the internet than this:
.org is meant to be used for non profit organizations...
...tell me: how many non profit websites do you think most people use, care about or visit daily? :)