Following my 1:60 rules of thumb, here are some rules of thumb that apply to altitude. Some of these, like pressure altitude, are basic stuff from any ground school, but some are not well understood. Density altitude is especially useful, because it lets you forget about all the temperature-correction interpolations in the performance tables in your POH and just read the numbers you need directly.
Pressure Altitude
OK, if you don’t know this one, stop flying. The altimeter setting for the standard atmosphere is 29.92 inHg (inches of Mercury). For every inch below that, your pressure altitude goes up by 1,000 ft; for every inch above, your pressure altitude goes down by 1,000 ft. Of course, the easiest way to figure this one out is to temporarily change your altimeter to 29.92 inHg and read the pressure altitude directly, but the calculation isn’t really trick. For example, if your altitude is 2,000 ft and the altimeter setting is 29.40, the difference from standard is -0.52, so you have to add 520 feet to get your pressure altitude (PA) of 2,520 ft.
Standard Temperature at Altitude
Standard temperature at altitude, at least below the flight levels, is even easier than pressure altitude, and again, everyone knows this from ground school. At sea level, the standard temperature is 15 degC, and it decreases by 2 degC for every 1,000 ft. So the standard temperature for 5,000 ft is 5 degC, the standard temperature at 10,000 ft is -5 degC, and so on.
Density Altitude
Density altitude is the key to airplane performance. For example, whether you are at 8,000 ft with an altimeter setting of 31.00 inHg and an outside air temperature of -23 degC, or at 2,000 ft with an altimeter setting of 29.00 inHg and an outside air temperature of 19 degC, you are at the same density altitude — 4,000 ft — and will see the same cruise speeds, the same climb rate, the same fuel consumption, and the same takeoff and landing distances.
If you have been muttering about wasting your time with the first two examples, here’s a chance to put them into practice: density altitude is, roughly, just pressure altitude +/- 120 ft for every 1 degC difference from the standard temperature at that pressure altitude. So if the pressure altitude is 5,000 ft and the outside air temperature is 30 degC, the difference from standard temperature (5 degC) is 25, and 25 * 120 is 3,000: that means that your density altitude is about 8,000 ft: your plane will be flying (and burning fuel) as if it was at 8,000 ft, not 5,000 ft; if you’re on the ground in the mountains, your plane will also take off and climb as if it were at 8,000 ft, so you might want to wait until the sun goes down and things cool off a bit.
Density altitude is also interesting in the winter, because it can drop thousands of feet below sea level, allowing your engine to produce far more than its rated horsepower. It’s easy to get spoiled watching your climb rate improve by 50% and your takeoff roll shrink to a few seconds, but remember that you’re also burning a lot more gas than you’re used to unless you throttle back a bit.
Takeoff Distance and Density Altitude
I’m not entirely sure about this one, so check your own manual, but in all of the POH’s I’ve looked at, takeoff distance is linear with density altitude: however many feet you add to your sea-level takeoff distance for 1,000 ft DA, you add double that for 2,000 ft DA, and so on. For my Warrior II loaded all the way up to 2,440 lb, the POH says that I need 1,100 ft of runway at sea level, 1,400 ft at 1,000 ft DA, 1,700 ft at 2,000 ft DA, and so on, so my magic number is 300 ft for every 1,000 ft of density altitude (of course, I always leave a big safety margin, and don’t fly out of short fields at full weight anyway).
Line of Sight and VHF/UHF Reception
If your thumb can do square roots, you can use it (or your pocket calculator) for figure out approximate VHF/UHF reception distance at any altitude, assuming the signal is strong enough and there are no mountains or tall buildings in the way. To get the reception range in nautical miles, multiply 1.23 * your altitude above the transmitter in feet. So, if a VOR/DME transmitter is at 1,000 ft MSL and you’re flying at 9,000 ft MSL, you can expect to receive it at 1.23 * sqrt(8,000), or 110 nm away.
Since VHF and UHF both work on line-of-sight, this is actually the calculation for how far away you can see something in clear air before the curvature of the earth blocks it. So on a clear night, this might also give you a clue about how far away you can expect to see a city’s lights. At 3,000 ft AGL, you might be able to start seeing them when you’re 1.23 * sqrt(3,000), or 67 nm away (of course, you may make out the glow reflected from clouds above the city sooner). Sometimes the atmosphere plays tricks and bends light a bit around the horizon so that you can see things even further, but I don’t claim to know enough science to explain that; if someone who knows writes in, I’ll add an update.
The Lying Altimeter
Finally, there is the issue of altimeter error. Temperature affects the density of the air (remember density altitude), which affects the pressure gradient, so on a hot day, the altimeter will say that the plane is lower than it actually is, and on a cold day, the altimeter will say that the plane is higher. The formula is 4 feet for every 1 degC deviation from the standard for every 1,000 feet above the station reporting the altimeter setting.
So, let’s say that you take off from an airport at 2,000 ft MSL (with its altimeter setting) and climb to 12,000 ft MSL to cross a 11,000 ft mountain chain. If the outside temperature is -30 degC, what’s your real altitude when the altimeter reads 12,000 ft? Standard temperature at 12,000 ft is -9 degC, so the difference will be 4 * 21 or 84 feet for every thousand. Since you are 10,000 feet above the station, you will actually be about 840 ft lower than your altimeter says — you’ll fly across the 11,000 ft mountains at 11,160 ft, give-or-take.
Land and Hold Short 
