I don't require formal teaching, in the "you have to find someone of this level and class to teach you before you can level up", but I do use the "general downtime" option/variant from the DMG, in that you have to spend at least 1 day per character level you're going to in non-adventuring duties; resting, training, studying, partying, whatever is appropriate for your character. This cannot be used for spell research or item creation or anything like that.
I like how this ensures that the party isn't out adventuring every day, and they do end up spending the occasional week or two just idle at their fort, healing up, relaxing, on vacation, or the like.
Now, if a player is going to learn a psionic or a primary divine or arcane magic class (other than being a Sorcerer or Wilder) they generally do have to be shown the basics of the class by someone with that ability (i.e. a Wizard, Cleric, Druid, Psion or Psychic Warrior as appropriate), and if you want to become a Monk you need to be taught by a Master (6th Level Monk, one nice use for the old 1e AD&D class titles) or spend some time at a monastery, and they'll probably have to spend time with you during your downtime teaching you. The basic idea being that you don't learn a whole new set of skills that is completely unrelated to what you already know and couldn't learn without some training without someone teaching you.
Exceptions to that "training" could possibly come up based on roleplaying and story, but I don't like characters taking a complete left turn with regards to their abilities and there being absolutely no story reason for it.