When is oxygen required at all times?

The three altitude steps

14 CFR 91.211 sets three cabin pressure altitudes for unpressurized aircraft:

• Above 12,500 up to 14,000 feet, the required flight crew must use oxygen for any part of the flight at those altitudes that lasts more than 30 minutes.
• Above 14,000 feet, the required flight crew must use oxygen the entire time.
• Above 15,000 feet, every occupant must be provided with oxygen.

Why Class A

Class A airspace starts at 18,000 feet MSL. In an unpressurized airplane the cabin is at the same altitude as the airplane, so anywhere in Class A puts the cabin above 14,000 feet, and the crew must use oxygen the whole time. Above 14,000 is the rule itself, and Class A is the only option that keeps you above that line for the entire flight.

Night flying

Part 91 has no night oxygen rule. The AIM encourages pilots to use oxygen above 5,000 feet at night and above 10,000 feet during the day, because night vision is one of the first things hypoxia takes away. That's a recommendation, not a regulation.

Passengers

The passenger rule starts higher, at 15,000 feet, and only requires that oxygen be provided. A passenger can decline it. The crew rules start lower and require the crew to use it.