It's quite a hardy plant with thick leaves that was in my home for a couple of years and it's growing like crazy. It grows small roots on its stems as You can see on the pictures and takes root in pots near it if not taken care of. Doesn't need a lot of water or sunlight, I don't think it ever bloomed but I might be wrong. Do You know what this is?
It looks and sounds like kalanchoe, a common houseplant. Yours is more leggy than normal, so it would probably benefit from stronger light. I've had mine for years, and when I put it outside in the sun, it grew big, thick leaves close to the ground. But it's good not to increase the light too quickly, and like you said, kalanchoe plants are easy to please.
I also think it is a kalanchoe, or rather, a plant of the kalanchoe genus. My kalanchoe plant has lived through years of terrible treatment. I went away for a month and a half in the summer and was sure it was going to die, but that is actually when it thrived the best! I came home to a plant full of the small flowers that form in a branching pattern. My kalanchoe also grew several other shoots and had the exposed roots like your plant so I either cut or pulled the shoots apart (I can't remember) and planted two of the "shoots" in separate pots and thus had three plants on my hands. You could easily make five new plants without making your original plant look scraggly. Between increasing the light, making new plants and skipping watering for a LONG time, you may end up with a sturdier plant with some flowers :)