I don't personally use them on my own blogs. However, I do manage a few sites where others use them for simply putting their "important" stories at the top of the blog page. Sticky blog posts seem to come in handy more often when you have news-style sites where there's a regular flow of new articles that might push an important one out of the spotlight.

Now, I do utilize sticky topics in my forums quite a bit for the same reason. It's not exactly the same WP feature, but the concept is the same. I think "stickies" are more dependent on the type of content a site uses. The more likely an important "post" gets pushed down from the top, the more likely one would use some sort of sticky feature.