Do US Universities commonly offer admission without funding? I am offered governmental scholarship (GSch) that I do not want to use for some reasons. I also don't want to lose the chance of PhD in a top university. I would use GSch, if I cannot get funded admission from a top university. Please read my previous question for more explanation of my situation.

My question is that do universities offer an admission without funding? So that, then I will have a chance to say 'I have another source of funding. Let me do PhD there'. For example, will I know I am in the waiting list? Do they put all the rejected students in the list? 

Or should I mention about the GSch at the first place? or maybe I should mention it only in applications of some universities.

Would I loose a good acceptance chance of mentioning at the first place, if I wait for rejection/waiting list decision?
Tough to predict how it will be handled with certainty. You could list the scholarship but then say in your SoP something along these lines: "I've earned in fact (a prestigious?) scholarship from my home government which would allow me to... however it comes with a requirement  that... which frankly I'd prefer not to commit to. Thus I would much rather be admitted with financial support from the university, in which case I would turn down the government scholarship."

For highly ranked research universities, I'd say it is not common for Ph.D. students to be self-funded. That said, if they can grab a strong student who is self-funded, what's not to like? :)