Can you post a puzzle without any hints so that the people find the answer without any help but using their logic only?
And that's only puzzles with the three top tags!
Also, hints should be supplementary: it should always be possible (even if hard) to solve the puzzle without looking at spoilertagged hints. So it's definitely OK to post a puzzle without hints at all.
This is indeed a rather broad question, but yes, such puzzles exist. We have a tag for it: enigmatic-puzzles
However, not all puzzles tagged like this will fulfil your requirement exactly.
I think the key-question is not necessarily if somebody can solve a puzzle without hints, but if it is clear what the goal is without specifying it. Take the following 'puzzle':
1 + 1 =
Very easy and you don't need hints. But only because you know what your task is, and that is because you pre-knowledge. Things like word-search are of the same category.
However, if you take this pre-knowledge out, your question becomes more interesting and rather philosophically, because why would anybody be interested in solving anything just because seeing it? You don't need any hints to solve a jigsaw puzzle, but again 'putting it together' is only clear because your brain demands a "complete picture". It wouldn't if you're only few weeks old...