I've always had a problem with the generic term "high magic", because there are just too many things that affect the level of magic in a fantasy setting.
There's the power of magic -- if Gandalf is one of the most powerful spellcasters in your universe, magic is far less powerful than a universe where Pug of Stardock is. It doesn't seem like most people object to the existence of powerful, world-altering magic in their games; 3rd-Age Middle Earth is a decidedly low-magic setting on this axis.
There's the commonality of magic -- how likely is it that a given person is a spellcaster? Are even minor spellcasters rare, like they are in the world of Glenn Cook's Black Company, or can almost anyone manage a few basic spells, like they can in Steven Brust's Dragaera at the time of the Vlad Taltos books. Standard D&D demographics say that less than 1% of the population are spellcasters -- and most of that less than 1% are adepts, which doesn't seem excessively high or low by the standards of modern fantasy.
There's the versatility of magic - Elmister, working within the confines of D&D magic, can accomplish almost anything; Melanie Rawn's sunrunners are excellent with communication, illusion, and fire, but don't have much else to go on. This is one area where D&D is definitely at a "higher" level than most fantasy; it's hard to think of something that couldn't be done with a spell, given a sufficiently powerful caster.
There's the distribution of magic power -- in Jordan's Wheel of Time there's everyone from the barely magic-capable Morgase Trakand to the heights of the Forsaken and a handful of others, with a cluster at the lower-midrange; the wizards of Terry Pratchett's Discworld don't seem to have much variation in power among themselves. Standard D&D demographics say there are half as many second level wizards as first level, half as many third as second, etc, which implies a pretty steep, but climbable slope.
And then there's the commonality of magic items, which is the thing that most people complain about when they say that D&D is too much of a high-magic game. And the high availability of magic items in standard D&D are almost unique. But I really think it's there for a good reason; D&D is a game, not a novel. If you've decided that powerful magic exists and is easily accessable by PC magic-users, then you either accept that PC magic-users dominate the game (Ars Magica), make quasi-magical abilities common (Earthdawn), or make magic items very common (Dungeons & Dragons). I think D&D's choice (to balance the wizard's spells with the fighter's magic sword and armor) is probably the best one for a quasi-medieval fantasy game.
