First, wizards do not gain new spells upon leveling per the rules. The only way for a wizard to gain new spells is to discover them in "the dungeon" or to trade for or steal them from others. This makes arcane magic, at least, that much more difficult to get hold of so that the players aren't pulling magic our of their orificies at every instant.
Magic is rare and mages are jealous of each other's abilities. This is to counteract some of the change below.
Casting still functions largely as detailed in the PHB. Wizards have a certain number of spell slots per day per level based on their current character level and any specialization they pursue (i.e., a transmuter gets an extra spell slot per level that must be devoted to an alteration spell). However, wizards can, with a percent chance of failure based on their intelligence and the level of the spell, attempt to "wing it" when casting spells. That means that they can forgoe memorizing a spell (or all spells for very intelligent and powerful wizards) in order to enhance their potential versatility. Unfortunately, this comes with a good chance of failing to successfully cast their spells.
Mages can still memorize their spells, and in fact, doing so greatly reduces the percent chance of failure.
A wizard with INT 15 has a base 65% chance to fail casting a 1st level spell while winging it. A 2nd level spell fails 70% of the time, 3rd 75% and so on. This means that our example wizard will fail 75% of the time while trying to cast a 3rd level spell without prior memorization.
If, however, the wizard in question chooses to memorize his spell in the morning, he reduces his chance for failure by 100%, thus in our example, the 3rd level spell is cast with a -25% chance of failure.
This, in actual play, does increase the utility of a wizard, but at the same time can make him somewhat unreliable. I can't tell you how many times I've heard "it's only a 10% chance of failure" right before a critical spell fizzles because the player wanted to leave the slot open "just in case."
It also has a very nice side benefit: players of wizards end up casting more of their spell selection (i.e., instead of just memorizing the same few over and over again) and there's fewer instances of "ok, we need this or that spell, but the wizard has to rest 8 hours before we can proceed, so everybody break out the bedrolls!"
A few other things to add into the pot:
For a specialist caster (transmuter, necromancer, etc), the caster receives a -10%/+10% failure chance based on whether the spell is in or out of their specialty school.
When leveling up, for every 5 successful times a spell is cast, the charcter gains a -5% chance to fail that particular spell.
At first level, and upon ataining further levels, the character gains 200% discretionary percentage points with which he can reduce any spell's failure chance, or he can hold them in reserve in anticipation of gaining new spells over the next level.
If, upon attempting to learn a new spell, the player fails the roll to learn, he can still scribe it to his book and cast it, but it suffers a +50% chance of failure. This can, and often does, raise the failure chance to above 100% making even memorized casting dodgy.
And one final bit:
A mage must still spend time every day reviewing and studying his spells. If his book is stolen or he has no access to it, he suffers an increased 5% failure chance per day without the book.
It looks a little confusing at first blush (and if I knew how to make this blog thing make tables, it'd be a might clearer) and it certainly does add a lot of book keeping to playing a wizard character or a bard (who follow the same rules, but keyed off of the average INT ahd CHA), but I find that the whole thing is definately worth it.
I like the falvor of it for Thylia, and since spells are rare, spell books cost 1000gp each, and the ink to scribe a spell costs 10gp per page written (not to mention 1 day per page/level of the spell), it's really a fair trade in my book.
Of course, I wouldn't try to port this over to Forgotten Realms or Greyhawk since I don't think it'd fit terribly well there, but in a grim and gritty setting where things are falling apart all over, it sort of fits.