This one has irked me since it first came out in Windows 95 -- I think that's when it was introduced. It even caused virus problems because users didn't know what type of file they were opening since the file would say something like, "ImNotAVirus.doc" with the ".exe" hidden. I never fell for anything like this, but I can see how people would. Yet, I'm amazed that this feature is still in Windows -- even in the latest Vista build. I don't necessarily have a problem with the option, but don't make it default to hidden. Maybe this is just the developer in me, but I can't stand when I can't see my file extensions. I just don't trust the system enough. This has nothing to do with my trust in Windows; instead, it is more about having control over file names.
Here's an example of why I hate it so much. Let's just say I want to create a new HTML file. First, I'll create a new text file via the context menu (right click > New > Text Document). When the file is created, I get the option to name it. With extensions hidden, you have no ability to change the name to "*.htm". This is just one example. Let's say someone wants to hide a file by changing its extension. Granted, not the best way to hide a file, but I've seen it happen.
Again, maybe it's just because I'm a bit more techie than most, but I absolutely despise this feature and can't wait for it to either be unchecked by default or die a slow death altogether... neither of which am I very hopeful for.