We've covered a lot of ground in this thread so far, and I thought it might be helpful to summarize some of the key points so far (or my take on them).
D&D presents rules suggesting a "high magic" world, one where magic is common, reliable, and flashy. A wizard's apprentice can cast Ray of Frost daily with no fear of unintended consequences -- and no doubt in any spectator's mind that he has cast a magic spell. Magic works like clockwork: observable, reliable, common, and not at all mysterious.
Many people would prefer a "low magic" system where magic is secretive and uncommon, where it exacts a price and leads to unintended consequences -- and where you're not always clear what's magic and what isn't.
Since the "low magic" people complained that D&D's magic system is bland and uninspiring, one of the first solutions offered was to spice up magic with evocative descriptions. Saying "I cast Magic Missile" is quite bland. Describing a flock of tiny demons winging toward your foe isn't. Good advice, but it still leaves us with wizards who can Magic Missile daily, at no real cost.
Another solution offered, pretty straightforward, was to restrict the levels played. At lower levels, D&D magic is...lower. If we want "low magic", this should solve our problem. But it doesn't. If D&D spells progressed from subtle to flashy, this would work quite well, but low-level staples include: Ray of Frost, Magic Missile, Color Spray, etc. And "low magic" staples include many higher-level spells that our low-level Wizards can't cast (e.g. Bestow Curse).
OK, that doesn't quite work, but what about replacing the core spellcasters with Oriental Adventure's Shaman class? This is actually quite similar to my own idea to shift around the spell lists, and I feel it could work pretty well -- it's a good start -- but I still feel you could get better results by hand-picking (as DM) an appropriate spell list. The Shaman's healing spells are still quite flashy, for instance. And the rest of the Shaman class doesn't necessarily fit a generic spellcaster; Improved Unarmed Attack would obviously have to go.
If we're going to set up new spell lists, how should we do it? Won't we destroy game balance? This opens a whole new barrel of monkeys. Is the current Wizard spell list balanced? Certain spells are much, much more popular at certain levels, and certain far less powerful spells are placed at higher levels.
For instance, Sleep effectively "kills" 2d4 Hit Dice worth of characters (who fail a Will save). Is it unbalanced to instead turn those victims into toads? Into statues of stone? Or to simply curse them until they find True Love or perform Herculean labors for the wizard (and probably die trying)?
This last example gets at another point that creeps into "low magic" versus "high magic": magic as plot device. Many of us would prefer magic that complicates the plot and provides new challenges, that offers something qualitatively different from the damage meted out by brave warriors with lances and swords. Ravenloft's curse mechanics, especially the twist of adding an Escape Clause to most spells, can turn magic into a story-generator, not a grenade-launcher.
If we move spells around and balance their power perfectly, we're still left with the problem that casters can cast a certain exact number of spells per day, they know exactly how many spells that is, and casting those spells has no other cost. If you can Charm Person "just" three times a day, is that any kind of limit? How can you explain a world where people have that power but don't use it every day? Is turning invisible for "just" half an hour a day much of a limit? How many banks could you rob?
There are a few ways to address to this. One simple change I've suggested in the past (but not in this thread so far) is to change "spells per day" into "spells per week" or "spells per month". This has little effect on dungeon-crawling spellcasters -- they clear out a dungeon in a day anyway -- but it explains why there's less magic in the world at large.
Or we can introduce a cost to "restocking" spell slots. Perhaps pious priests need to perform tasks for their god. Perhaps evil sorcerers need to spill innocent blood for their demon patrons. Perhaps the wizard needs to gather up herbs at midnight of Midsummer's Eve. These costs can naturally lead to more adventures and drama.
Or, as others have pointed out, we can force some kind of spell roll for spellcasting. Virtually every other system requires it. Failing the roll doesn't have to mean watching the Fireball fizzle. It can exact a game-mechanic cost on the caster (subdual damage, Con damage, damage to all abilities, cumulative penalties to any further spellcasting), it can mean unintended consequences (polymorphing someone else too, or changing into the wrong animal), whatever you want. But it does explain why magic would be saved up for special occasions, and it hopefully leads to more exciting stories.