There have been so many topics dedicated to this very question (кое-, -то, -либо, -нибудь). Try searching for some of them on this forum.
Briefly:
Я хочу кое-что спросить. - I want to ask something, and I know what it is, but I am not telling you right now (maybe I'll tell it later, but at this very moment it is like a secret or a surprise).
Я хочу что-то спросить. - I want to ask something, and I do not know what it is (does not make too much sense in this context).
Я хочу что-нибудь (что-либо) спросить. - I want to ask something, and I do not care what it is (just anything).

The following example gives more clarity:
Он по утрам кое-что читает. - In the morning he reads something. I know what he reads. You do not know. For some reason, I am not telling you WHAT he reads.
Он по утрам что-то читает. - In the morning he reads something. I do not know what he reads, I only know the fact he READS something.
Он по утрам что-нибудь читает. - In the morning he reads something. Different stuff: today this one, tomorrow that one etc. Just anything. Whatever.