Most birds fly below 500 feet except during migration. There is no reason to expend the energy to go higher -- and there may be dangers, such as exposure to higher winds or to the sharp vision of hawks. When migrating, however, birds often do climb to relatively great heights, possibly to avoid dehydration in the warmer air near the ground. Migrating birds in the Caribbean are mostly observed around 10,000 feet, although some are found half and some twice that high. Generally long-distance migrants seem to start out at about 5,000 feet and then progressively climb to around 20,000 feet. Just like jet aircraft, the optimum cruise altitude of migrants increases as their "fuel" is used up and their weight declines. Vultures sometimes rise over 10,000 feet in order to scan larger areas for food (and to watch the behavior of distant vultures for clues to the location of a feast). Perhaps the most impressive altitude record is that of a flock of Whooper Swans which was seen on radar arriving over Northern Ireland on migration and was visually identified by an airline pilot at 29,000 feet. Birds can fly at altitudes that would be impossible for bats, since bird lungs can extract a larger fraction of oxygen from the air than can mammal lungs. http://tinyurl.com/2ewlxw

According to the U.S. Department of Energy, Zoology Archive there is an incident of a Ruppell's griffon, an African vulture, struck by an airliner at 37,000 feet. Mallard ducks routinely fly at 12,000. It's a function of wind currents, thinner air (less wind resistance at higher altitudes), etc. Oviously your non-migratory and/or garden birds like cardinals have no reason to behave in such a fashion.