It looks like a Senecio, possibly Senecio vitalis. Have you had flowers?

I have Senecio mandraliscae, Blue Chalk Sticks, growing outside. They are not as erect as your plant, and in fact seem to sprawl along the ground. So I'm not really sure if yours would eventually lay down in nature, or if you need to do something, like prune and propagate, to keep them tidy. Perhaps they grow tall with a bushy top, like a shrub. Maybe it needs more light, but it doesn't really look etiolated.

I hope someone else chimes in. It looks like a nice healthy plant.

Thanks! No flowers in the past few years...and no sign of flowers to come. It does want to lie down...maybe I should stop propping it up...?

It's got to be a Seneca vitalis! Now I just need some imput as to how I shoud better care for it! Any ideas?

I would definitely clean up the parts that have died. If they fall to the bottom they can grow mold and destroy your entire plant. I would also maybe consider propagating. It doesn't appear like you will be getting any new growth on the bottom.

What is the best way to propagate? I have read it's best to wait until spring