There is no such thing as 220 in the United States. In other words, there are 2 hot wires and each must be protected. If you're lucky enough to have 3-wire outlets, then you can save one outlet by using a split 120-volt feed from one circuit to two different locations.
However, this is not recommended for appliances that use much power: lamps, heaters, air conditioners. These devices should always be connected to a 3-wire circuit so they can operate at full capacity. Otherwise, you'll be asking for trouble when they need maintenance or repair.
The only time I would recommend removing an outlet from a 2-wire circuit is if you have a 4-wire system and want to connect it to a 3-wire outlet. Then you can remove either outlet from the circuit and the other will still be live while allowing you to use all three connectors on one device. This can be useful if you have a lamp plugged into one of the removed outlets and need to turn it off from another location without unplugging it.
However, keep in mind that if you disconnect both outlets from a 2-wire circuit then neither one will be protected and anything attached to them will be at risk of overheating or catching fire.
Only if, as Steven points out, there is a split 220 volt line with a two-pole circuit breaker. This guarantees that the circuit has two distinct legs rather than simply one. In addition, with only one breaker, the entire circuit will be turned off. If something on one leg of the split circuit breaks, everyone else on the circuit could be affected.
The answer to this question depends on your wiring system and local code requirements. If you're using a three-wire 120-volt system, such as an old-fashioned North American one, then no, you can't share a breaker between two separate circuits. The reason for this is that modern electrical systems are designed to protect people from dangerous currents by shutting off the power before it causes injury. If you shared a single breaker between two different circuits, it would be possible to shut off one circuit while the other one was still energized which would put people at risk.
On the other hand, if your town uses four-wire 240-volt service and separates neutrals with wire connectors instead of cable ties, then you can indeed share a single breaker between two separate circuits. The neutral connections of each circuit would then be connected together on one side of the breaker and the other neutrals would be connected on the other side. Since electricity cannot flow through neutrals, this configuration ensures that if anything bad happens to any one set of wires, the others will be disconnected too.
When you have a 220v item like a stove or an AC that takes two phases of electricity to get to the 220v, you'd normally utilize a double pole breaker in the US 110v system. If you wish to use it on a 110v single phase circuit, you may utilize a double pole breaker. However, all modern double pole breakers will also function on a 120v circuit.
The main reason for using a double pole breaker is so that if one pole gets damaged, you can still supply power to the circuit. On a single pole breaker, if one wire gets disconnected, then the whole circuit goes out. With a double pole breaker, each pair of wires has its own separate breaker which allows for some redundancy in case one of those pairs gets broken.
There are three types of double pole breakers: magnetic, electronic, and thermal. Magnetic double pole breakers are the most common type and work by utilizing two separate magnets to open both poles of the breaker at the same time. Electronic double pole breakers are similar to single pole breakers but instead of using magnetic forces to activate their contacts, they use current sensors to determine if a circuit is closed and if not, they will open themselves. Thermal double pole breakers use the heat from a burning component to activate their mechanism which in turn opens the circuit.
Magnetic double pole breakers are the most common type because they're easy to install and cost-effective.
A 220 volt circuit is double-pole and requires two slots. Tandem circuit breakers, which place two 120-volt circuits in one slot, offer a remedy for this problem. The first breaker to trip will cause the entire panel to shut off, so make sure that both breakers inside the panel are tripped simultaneously.
Tandem breakers are available with thermal units that automatically reset themselves after a predetermined time delay. These breakers are designed for use on 240-volt circuits and should be used only on permanent wiring. Do not use them on 120-volt circuits or they may fail to operate when needed.
Tandem breakers are more expensive than single-pole breakers but they do save energy because their separate circuits don't have to be turned on simultaneously to provide electricity to the load.
The main disadvantage of using tandem breakers is that if one breaker trips then all power is lost to the panel. This means that you need to ensure that both breakers inside the panel are operated simultaneously by an external force before replacing them with a single-pole breaker.