Nonhuman animals? No idea. We don't even know how to phrase the question rigorously, let alone how to even conceptualize answering it.
I think the key thing is qualia. That is, there's some subjective experience. If you prick us, not only do we bleed, but we feel it.
This is pretty vague, which is the whole problem. But if you feel it when you're pricked, you know what I'm talking about.
This can't be measured or even observed except from the inside. Nobody even has the slightest idea of how it could be measured, even theoretically. The existence of this phenomenon in people other than myself is something I have to take largely on faith. (But, as I mentioned, not entirely, since the existence of this concept shows at least some other people have it.)
The main reason I think this is because there are people who don't seem to get the concept. These threads often have people arguing that consciousness is no big deal, it's just your brain making decisions based on sensory input, etc. I can't imagine an entity with qualia making that sort of argument. This might just be a failure of imagination on my part, but that's what it looks like.
It's very tempting to apply this idea to e.g. idiots who stand in the middle of a doorway and chat while others struggle to get past them, but I recognize this is just an irrational desire to diminish people who annoy me in the moment.
When you say "almost all," is that just to accommodate people in comas and such? Or does that mean you also think there are people who are walking and talking but don't have consciousness, and you just don't think there are very many?
I believe we are all just bags of chemicals playing out the laws of physics, no libertarian free will at all. Consciousness is an orthogonal issue. Humans have it, and if you have ever lived with a dog you'd agree they have it too despite not being verbal ... hell, it isn't rare for humans to have no internal dialog yet nobody would say they are not conscious.
Consciousness is a continuum and there is no bright line where it starts/stops. Bacteria react to their environment but they are conscious in the same way that one minute after shaving I have a "beard" -- technically the hair stubble rises above the surface of my skin, but it isn't a beard. Wait a month and clearly I do, but there is no bright line where I transition to having a beard.