Who's in control here? You're the one moving on, right? Don't worry so much. :)
If your boss is out of the country, dealing with a family emergency, or otherwise has a serious something going on, I would extend the same sort of time off courtesy that the employer would extend to you in the same circumstances. There are times when you're not expected to be dealing with work related things, so reflect that courtesy to your boss. They have a right to be gone occasionally too.
If that's not possible (perhaps you've already accepted an offer at a new place, and you've committed to a start date), then you might want to talk to your boss' boss, or someone in HR if this is truly some kind of emergency or time sensitive notice that you need to give. Someone above you must be working at the company, and so long as you make it clear that you tried to go direct to your boss first, and explain why that's not an option this time, it should be okay.
Most of the rest of the time, it's professional to be professional, and a bit patient.
Still give notice.
- Diplomatic / asked to wait
This happens. Any boss would want to know what's going on, especially if they want to try to convince you to stay. After all, talent acquisition takes time and you don't want to lose people unnecessarily.
That said, you can still give notice politely, but firmly. If something is really wrong and you've been in regular communication with your manager (say, a big shakeup in the management happened, or your company was sold, etc.) then it shouldn't be a shock if you're heading out. That doesn't mean they won't make a final pitch to keep you. This is not a bad thing.
Still give notice.
- Asked to delay for boss' boss' opinion
You're the one making the decision, not them, so I don't see why the speed of decisions at the management level plays a role here. Assuming you're not working in a sweatshop/indentured servitude/slavery situation, I don't see what "permission" you might need from anyone at the organization, so what decision is there to be made? If this is happening it may just be a delay tactic to pitch you to stay.
Be professional, and give whatever length of notice is customary to your industry / locale, and let it be.
Still give notice.
Unless you don't need or are somehow sure that you won't at some point want a reference from these people, then always give notice. Don't be so short-sighted as to circumvent whatever conventions are the norm in your industry. It might be taken as a slight, and while it's a minor inconvenience, there's no point in taking a long-term hit for what is a short-term inconvenience.
If you don't give notice, don't expect a positive reference. That may not feel fair if you believe you really put in a lot of time and/or effort at a place. But hey, people are people, and life isn't always fair. Generally my policy is, "Don't burn a perfectly good bridge for no reason." If management isn't professional enough to accept a reasonable notice and move on, then leaving too quickly won't fix anything either, so either way you don't win anything by leaving without notice.
I wouldn't interpret them trying to slow you down as unprofessional necessarily. Like I said above, if you're one of the more senior people in your role, and if the working relationship has been great up to this point, then they might not want to lose you. As a result they may try to delay. There are a ton of other context-specific reasons they might delay, but you're the one making the decision, so be sure about it.
Just suck it up and give notice if you want to be taken seriously as a professional, even if the working relationship isn't a good one. Time heals whatever wounds you may be feeling at the moment.
