I know that when planes enter the aerodome containing the airfield of destination, the ATIS will tell them an altimeter setting so the system knows how to calculate their altitude above their field; what about in cruise? Do they listen to the ATIS of every sector while cruising as well?
Above Transition Altitude (e.g. this is 5000ft in Germany) the altitude is measured in flight levels (FL) - each FL equals 100ft and is measured above an artificial QNH of 1013,25 hPa. If you cruise for example at FL380 that will be 38000ft above the pressure level of 1013,25 hPa. This system assures that 2 aircraft which are 10 FL apart (e.g. FL370 and FL380) always have the required separation of 1000ft. During descent when passing Transition Level you will change your altimeter setting to local QNH which ATC will tell you.
To combine the other two answers:
Below the "transition altitude" (which is 18,000 feet in the US, 5,000 feet in Germany), the pilot has to pay attention to the current altimeter setting, and adjust it accordingly. However, they don't have to listen to ATIS/AWOS/etc., most controllers will give you the current altimeter setting when you check in with them, or when you make some request, or when it changes, or sometimes just for no reason at all. If you're not talking to ATC, though, you would have to get the local altimeter settings from ATIS, or satellite weather, or some other source.
If you're above the transition altitude, however, you are supposed to just set your altimeter to a fixed 29.92 inHg or 1013 hPa. The theory is that when you're that high, the distance to the ground doesn't matter. There are no towers to avoid or anything, so you only need to pay attention to the distance between planes. Having one single setting helps relieve the pilots of fast-moving planes from having to constantly adjust their altimeters while still providing vertical separation between aircraft.
In a word: altimeter. It is a device that measures the pressure of the atmosphere. Flight levels are expressed as height above Mean Sea Level or MSL, a worldwide standard of pressure at sea level at a specified temperature or "standard temperature and pressure". The referenced altimeter reading is actual pressure at the surface.
Altimeters in aircraft can be adjusted to compensate for local variations in the air pressure so that altimeters in all aircraft display approximately the same readings at consistent heights above the surface in the area. Periodic pressure references and adjustments are necessary as air pressure fluctuates due to weather patterns.
Air traffic controllers usually give periodic altimeter settings, especially when first contacted during communication hand-offs. Pilots may also request that information from them. Other sources are ATIS, if a tower-controlled airfield is nearby, En-route Flight Advisory Service (EFAS), and automated weather reporting stations such as ASOS and AWOS.
When attempting to land at a controlled airfield, a wise pilot will listen to the ATIS prior to contacting the approach controller. In instrument conditions, having an accurate altimeter setting (among other things) is critical to operating and landing safely.