"depends on" usage

I think it's possible. I usually leave it out when "It depends" is just a way to say that a certain statement is not true in every case or for everyone.
Is a Ferrari the right car for me? It depends how much money you have. If you are really rich, you can afford it, and you like it so much, why not?
And I don't usually leave it out if "depends" is part of an explanation, and what follows is what a certain thing relies on.
The speed of this new rocket depends on which coefficients have been chosen when designing the outer parts.

But maybe it's just me... I'm not a native speaker.

Hi,
I don't know, it's just the way I use it. I don't include "on" when I use the expression "It depends", where "It" is not really referring to something specific. I could leave out the part after "It depends", in those cases.
Is it good? It depends (what you mean by good)
I don't know if I'll be there. It depends (whether I'll feel like it)
You think I'm handsome? Heh, it depends (who you are comparing me with)
Here you have something more specific, where I can't leave out the part after "it depends".
We are talking about the parameter alpha. It (=alpha) depends on how we choose the other related parameter, beta.

In any case, I think I can't make a clear-cut distinction in every case, so there are several cases where I'd just say the version I like better. Also, this applies to "it depends". If I change the subject, and say "That depends", I am much more likely to include "on", I think.
Just my opinion.

You can always use on.  depends on.

But when the subject is it and an indirect question follows, you can omit on, but you don't have to.  It depends (whether / what / who / where / when / how) ... 

Note:  It depends on the first person to arrive.  (You can't leave out on here.  There's no indirect question.) 

Personally, I always use on.

CJ