I don't like them. With a screencast I have to sit through it at the pace of the presenter. With an article I can read at my own pace and skim it if needed.
ETA: Good point below, screenshots enhance an article more than a screencast would, for me anyway.
I find a written document, perhaps augmented with screenshots, to be most helpful. Screencasts, by themselves, I find to be next to useless. A screencast demands investment of significant time before one can even determine whether its going to be helpful. With a written document, it's usually possible to tell from the first paragraph or a quick skim if it's something worth spending more time on.
Screencasts are undoubtedly faster and easier to prepare than a written document, perhaps that's why I tend to see so many involving technologies such as CMS platforms that cater to folks who want quick solutions that they don't need to understand very deeply.
ETA: Good point below, screenshots enhance an article more than a screencast would, for me anyway.