Most stickied threads are made by those who are capable of stickying a thread.
Usually that's the case if the user has the intention of the thread being important and informative.
Sometimes, however, a mod or an admin will see a thread that they believe deserves to be seen by everybody and/or is important enough to be at the top of the page. There are a couple of stickied threads made by regular users still floating around in the forums.
Einfach and I each have a stickied thread in here. And there are several other stickied threads in a few other sub-forums. Basically, they have to be relevant to the sub-forum and very helpful. Sometimes making something that gets asked a lot will get stickied. Like my Exit Path Guide, I was in the Game Walkthroughs sub-forum a few months ago and I noticed a lot of people asking about Exit Path, they would ask in the Flash games sub-forum as well, so I created an Exit Path Guide, Ashleree saw it, then she stickied it.
But if I got some thread I want to be stickied, should I ask a Mod then?
You could, but in general asking for something is the sure-fire way of not getting it.
It's not about wanting something stickied, it's about the thread being deemed appropriate of getting the treatment. Most things that need stickying have already been stickied, so you're pretty hard pressed at the moment.
Asking for a thread to be stickied will *likely* be turned down, unless it's something really earth-shatteringly helpful to the community at large, or immensely popular. Though 'opular' threads tend to get enough replies to stay on page 1 or 2 of a forum anyway...