It seriously depends on the character and what one call's specialization. My current character Akemmi is a hybrid, she uses magic more, but also melee skills, smithing and enchanting ( I do keep them well balanced). I would call my next character Kurdan a specialist: dual wield, archery, light armor, smithing, unperked speech. But if a some point it makes sense for Kurdan to learn Alchemy or Restoration, then he will... For me though it can't just be because ummm Stendar's Arua is an awesome tool to use fighting Vampires or a Paralyze potion would make getting through XX dungeons soooo much easier, those things have to make sense... would he use them? Why? Can he learn?
The skills my characters have must fit into their lives, into their story... personality...education...etc. I generally set a "guideline" in the form of a backstory for my characters, that doesn't mean they can't grow and learn... they just have to have valid reason's why they would do so. As I live in a college town, I could go take a course in....land management... why would I do that though? Yes I live on a ranch... I rent space... but my job is in retail management.. their is no Earthly reason for me to take a Land Management course... except for the heck of it.... a complete waste of money. That is what I mean when I say my characters have to have sound reasoning.... if they are a few egg's short of a dozen, then nothing they do is rational.
Edit: I prefer no limit's except what I give my characters. Now on the other hand.... quest limitation would be fine with me... meaning my Melee, heavy armor, no magic using Dragonborn, shouldn't be able to be Arch-mage or Listener. I think one should have to have high skills in those fields ...but that would be a limit and if it couldn't be implemented well, then.. I can use my imagination to limit myself.