the best textbooks could perhaps be just as good a replacement, like all the books mathwonk as mentioned (as well as asking questions on forums). You get the best of both worlds. After studying a subject, find an online exam or test, and time yourself. See if you do well. This will gauge whether your self study was good. Or just make up your own exam from problems randomly selected from the book or other books.
Of course, the ideal situation, as arildno says, is 1-1 study with a professor. You would probably become an expert in the subject in a very short amount of time. Also you don't have to go in a linear order when studying. Sometimes jumping ahead, and getting the big picture, will allow you to gain a better understanding of earlier concepts that seemed difficult.
But with forums, you get input from both experts (like mathwonk, matt_grime, Chris Hillman, etc.. arldino, all the mentors, etc..) and students. So these different perspectives only aid in your learning experience. So really you would learn the most from a collective group of people like those in this forum.
Sometimes self study will spark creative thoughts/ new ideas. It forces you to come up with your own perspectives of a subject. Thus, you learn the subject at a much deeper level. A formal classroom environment may stifle this. Of course, the opposite could be true.
I recently e-mailed Edward Witten, and asked him what he did. He said that he self-studied most of the physics. But he would still recommend a formal classroom environment. Its an easier track.
Most professional mathematicians learn other fields from their co-authors. So this emphasizes arildno's point about 1-1 study with an expert (or experts) being the most efficient.