The most important piece in any videographer's arsenal is, of course, the camera. It's the one piece of gear you are going to use no matter what, so do yourself a favor and get the best camera you can afford. After that, then what? What is most important accessory? I'm going to rule out audio since that's a category in and of itself. My gut reaction is a tripod, but I'm going to go out on a limb here and recommend something you might not think of, but can prove invaluable: a wide angle lens.
Just about every video camera made (even really cheap ones) has a set of almost invisible threads that allow the screwing in of external lenses. Most will never want or need these, but a wide angle lens is so useful, you will always want to have one handy. I have found myself in many a tight space (small room, alley, hallway) that looks claustrophobic with the stock lens, but really opens up with the wide. You get more depth and more of the surroundings that you weren't able to see before. Tracking shots in aforementioned narrow places look great when shot this way.
The tradeoff is now that you are bending more light to see more, you will also get distortion. This is most evident when shooting the human face. A wide angle lens up close is very unflattering (and a super-wide or "fish eye" lens is downright disturbing) so remember to keep your distance. Another problem is that you can see the edges of the lens when zoomed all the way out. This is easily fixed in post by simply cropping the image.
I love the wide angle. I use it all the time and find that it allows me to shoot in more places, that just wouldn't work otherwise. They come in every size (you may need a step-up ring if your stock lens is non standard) and are pretty affordable, so why don't you have one?