Identifying a Houseplant?

I have had this plant for almost 10 years now and have no idea what it is or how to best care for it. When I got it, it was just a tiny thing that could sit on my desk and it had no height. Over the years, it's grown taller and taller, but the stem? stalk? trunk? seems kind of dead towards the bottom and the bottom leaves end up dying and falling off.

You can see where it is green in the middle and the leaves grow from the top. It also zigzags on its way up and I wonder if it's because I'm supposed to cut it in those places and replant it. I just don't know what to do. I looks kind of sad, I think. Am I supposed to plant it deeper? I guess the first step is to figure out what it is exactly and then how to handle it. I think it may be some kind of dracaena, but I don't know anything about plants at all.