Actually, the only puzzle I truly figured out on my own was Square-1. I started learning to solve the 4x4x4 on my own in 1998, but got stuck at OLL parity. I had no understanding of what parity was at the time, so I gave up and searched for an algorithm online for how to solve it. I did "figure out" the reduction method with minimal input from other 4x4x4 solvers and one website at the time, but I learned parity. 3x3x3 I completely learned from a website, no independent thought whatsoever :-( :-( :-(
I feel like all the rest of my puzzles were "tainted" from me learning the 3x3x3 so I don't count pyraminx or megaminx even though I solved them without help (but used 3x3x3 concepts from my 3x3x3 methods).
By the time I got around to Square-1 I was determined not to give up. I spent about a full week coming up with a method for it, and it is slow as hell and super inefficient, but it works well enough to place me 318th out of 362 competitors for fastest single (as of 4/17/09) haha :-D
One day I may try to either improve my SQ-1 method or learn a new one, but for right now it is my only puzzling "victory" of figuring out a puzzle completely on my own with no help at all from any person or website related to the puzzle. I suppose you could say that even this is "tainted" because I do solve layer by layer, but I came up with my own parity fix algorithm (terrible and super long, but it works), my own algorithm to solve edges and my own algorithm to cycle corners.
Chris