Having read the various posts on Vancian magic, the stories that inspired the system, and some of the criticisms of the same, several thoughts have come to mind:
1. The core ideas -- that spells take up mental space, and that human mental space is limited -- can easily be rationalized in a setting. Whether it is because one can only memorize so many spells in a day, or because spells are semi-living things that take up certain amount of finite mental space in their hosts, or because spells are complex mathematical formulae that can be pre-cast in a finite amount of time and released with triggers, if that's the way magic works then it should be accepted as part of the setting... just like half-elves, massive underground dungeons, and a mysterious mint that continuously strikes generic gold, silver, and copper pieces for placement in treasure chests.
2. The criticism of Vancian magic seems to stem from the very specific mechanics, which vary from the portrayal of magic in stories and media that we're exposed to. In the Harry Potter universe, magic does require some learning, but once learned the spells seem to be castable at will -- and there are consequences for miscasting. In the Belgariad, the most common price of magic is to tire out the spellcasters, but there seems to be no restriction on which spells are available on a given day.
3. The wizard class itself seems to be restricted, given the restriction on swords and other weapons and armor -- which runs counter to the portrayals of spellcasters in fiction. Gandalf, of course, wielded a sword; while he may be characterized as a multi-classer, he didn't seem to be much of one and is still held up as a classic example of a wizard.
It seems that a lot of the criticisms, and the attempts to fix the magic system and magic-user class in general stem from the perception that D&D mages aren't really very generic despite their portrayal in the art.
Now, I've read somewhere in magazines (forgive my memory, this was 15 years ago) that there used to be a magic point system in the very early days of D&D, but there was a terrible effect on gameplay: mages became spell-slinging machine guns, which robbed the RPG of the flavor of mages.
These days there are many magic systems with different mechanics out there, so issues #2 and #3 are easily fixed (3E and 4E have both taken stabs at it, as have other retroclones).
How successful have they been in retaining the feel of a mage or wizard, despite / because of the chosen mechanics?