I was thinking an apprenticeship would be a more common trope, but couldn’t come up with any examples. Which I guess is understandable since I’m not familiar with any that you listed. That’s kind of what made me wonder about this, Ged in “A Wizard of Earthsea” started as an apprentice and then ended up in school.
Given the other stuff you’ve read, that’s a bit surprising. For reference, Skeeve is the protagonist in Robert Asprin’s comic fantasy Myth Adventures series, Harry Dresden is from Jim Butcher’s Dresden Files (a currently ongoing urban fantasy series), the Gray Mouser is from Fritz Leiber’s old-school (1940s-1970s) sword and sorcery stories, and Pug is from Raymond Feist’s Riftwar Saga. I thought they were all pretty well known.
John Constantine, from the Hellblazer comics, is a talented wizard who never received any sort of formal training, either academic or apprenticeship. He’s picked up a lot of tricks by hanging around other magicians, through independent research, and signing the occasional demonic bargain.
The Rose of the Prophet trilogy had “western” (pseudo-European) wizards going to ‘traditional’ schools/universities to learn their trade. The pseudo-Arabic nomads had magic, but it was only done by women, was more informally taught within the tribe and was far less powerful than their better schooled counterparts.
Edit: I don’t know that the “western” schooled mages had singular apprenticeships so much as being “underclassmen” or “graduate students” of sorts. One of the principle characters was a student among a group of students chosen to come along on a voyage as a special privilege for their hard work and promise.
Skeeve spends most of the series in a one-on-one situation with Aahz (though the line of which one is master and which is student blurs considerably, and Skeeve also takes on an apprentice of his own), but towards the end of the series, Aahz does arrange a correspondence program for him with his own alma mater.
In Diane Duane’s “Young Wizards” series, a Wizard’s education is intensive but rather informal; wizards have access to magical ‘Wizard’s manuals’ or other information sources that give access to all the information relevant for their current circumstances and skill level. They also routinely consult with higher-ranking Advisories and Senior wizards who guide their education and help them figure out what specialties they’re interested in and what sub-specialties to research next. Diane’s compared it to a decentralized grad school system, with the Advisories as faculty and Seniors as local deans.
Standard nowadays, but it’s relatively recent, compared to the apprenticeship model. See the TVTropes page on Wizarding School.
As one who writes quite a bit of it, I prefer the term “arcanobabble”. 
In “Master of the 5 Magics” Alodar starts out as an apprentice thaumaturge but later learns the other 4 magic systems. IIRC alchemy and magic had schools and the others you just had to find someone to teach you.
Brian
That seems more in keeping with Tolkein. Unless you’re a hobbit, you have to be born to greatness - greatness is not something a regular person can aspire to on their own.
In one legend, Merlin is the son of a demon and a virgin, intended to be the Antichrist. His mother informed Blaise, her priest and confessor, and he baptized Merlin at birth, driving out the demonic influence. Blaise thereafter served as Merlin’s tutor, but as a priest, he would not have been teaching him magic.
That was a pretty good book.
For those two, schools (or some large, organized approach, at any rate) seem pretty much inevitable.
Magic–that is, the specific domain of magic the characters called “magic”, and which I might call “enchantment”–is an extremely fussy business in that setting. It takes a lot of resources and effort to accomplish anything of interest with it, so it makes sense that schools would form. Pooled resources and lots of neophytes to fill roles at ceremonies enabled them to make stuff they otherwise couldn’t. Alchemy benefited similarly, relying on a mass-production approach to overcome the problems of refining ingredients and making products with a relatively low individual success rate.
Gandalf was never born.
This is not just a matter of fiction. In medieval and renaissance times there were real people who aspired (fruitlessly, no doubt) to be magicians and (what is not very different) alchemists. A great deal of their search for magical powers revolved around book learning, the seeking out of obscure manuscripts, the deciphering and interpretation of extremely cryptic texts, and so forth. It is no accident that most fictional wizards fit more or less the same template. (Tolkein’s wizards are an exception, but then, “wizard” is not really the ‘correct’ word for them.)
I’ve heard of the authors you’ve listed and I caught an episode or two of the short lived Dresden file series on TV. And to be perfectly honest, I knew I’d get some good ideas on what to read next from this thread. Looks like Dresden Files and Riftwar are going on the list.
Indeed, and that’s true (I think) even before we had the shift from the “apprenticeship model” to the “university model” of wizardly education. Part of the shift reflects the change in the way we’re educated, true–but wizards pursue a particularly “academic” career, half-chemist, half-applied philosopher. It’s only natural that they would tend to be produced from schools or universities nowadays, rather than say, fighters or thieves. (Though Mary Gentle’s Rats and Gargoyles did feature an, IIRC, “University of Crime,” an idea I’ve always found strangely appealing. This is what you get for being mildly ganef-besotted like I am.)
IIRC, at one point he goes crazy and lives naked in the woods as some kind of wildman for a period of years. When he eventually regains his sanity, he can speak the language of the birds and beasts and other nifty nature-based powers.
Some versions of Merlin have him being a druid, and learned magic through them. Not sure how far back that idea goes, I suspect it’s fairly recent. One series of books I read (name and author escape me at the moment) tried to put as much of the Arthur mythos as possible into a historically accurate (but still fantasy) framework. In those novels, Merlin is the son of Taliesin, the semi-mythical Welsh bard, and learned his magic from him.
I think the shift from the apprentice model to the university model in fantasy literature is connected to changes in the genre itself. Based on what I can tell, up until the 1980’s most fantasy stories, inspired by either Tolkien or Howard, were set in analogues to Early Medieval settings - pre-1100 AD or so. In such a setting, apprenticeship is the only option. In recent decades, though, many fantasy writers have been moving away from Middle Earth/Hyboria and inventing worlds that are more High Medieval or even Renaissance in tone. Here, universities have a place - and if anyone’s going to be going to university, it’s going to be wizards.
Naturally, there are exceptions, like Ursula K. LeGuin (although note that Earthsea is the rare non-European fantasy world). Still, it seems to me that current fantasy writing involves fewer mighty-thewed barbarians and more burghers.