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I high school (early 80s) I bought and pretty much memorized a book and was able to do it in just under three minutes.
But now I take them apart and reassemble.
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I can solve with in 5 minutes. 
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It's often cited as the world's best selling toy. By 2009, 350 million cubes had been sold, nobody knows how many pirate versions had been sold but the number must have vastly outweighed the number of legitimate ones.
Which begs the question of how much plastic has been consumed by one not-so-simple puzzle and how much of an ecological impact Professor Rubik's brain-wave has caused. Somewhere there must be one of those "amazing facts" regarding what would happen if all Rubik's cubes were stacked into a single cube and how many times the size of Wales it would be.
So far there are only 5 of 105 poll respond here who have never heard of the thing - considering that it peaked in the early 1980's, that's quite something.
Whenever you find yourself on the side of the majority, it is time to pause and reflect. - Mark Twain
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I think everybody I talk to have learnt it from a book algorithm. I figured out my own (rather inefficient  ) algorithm in my teens. Never looked at the book algorithms. How many like me?
"If we don't change direction, we'll end up where we're going"
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I'm like you, I figured out my own not-too-brilliant approach (basically getting the corners in place by deduction and brute-forcing the rest of the cube). It will never win prizes for speed but it does always get there in the end.
Whenever you find yourself on the side of the majority, it is time to pause and reflect. - Mark Twain
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Yes I basically had "sequences" that worked in pairs:
Flip one corner on a face
Flip another corner on the same face (in reverse order, to restore the rest)
The same for swapping corners, and the same for the "mids"
"If we don't change direction, we'll end up where we're going"
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Almost. I'd get 4 corners (and centres) then try to get 8 corners with a basic right-handed sune (RUR'URU2R'), which twists but does not swap corners. If I couldn't get all 8, I'd cheat by scrambling and trying again. The edge bits were simple in comparison. Over 5 mins by myself, getting it under 1 minute (my record is 24s) needed internet help, as did swapping corners. I keep one on the sofa for use during adverts 
Pete Lomax
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I figured it out when it first came out. It did take me several weeks, but eventually I managed it. The problem was always remembering how to solve the last layer. I have one sitting on my end table and solve it every now and then, to keep it fresh.
INTP
"Program testing can be used to show the presence of bugs, but never to show their absence." - Edsger Dijkstra
"I have never been lost, but I will admit to being confused for several weeks. " - Daniel Boone
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I carefully observed what happened when I made combinations of turns. The "proof" that I didn't use the book is that I solve first Top, then Bottom, then fill in the middle pieces. The book teaches you to solve it top to bottom.
<sig notetoself="think of a better signature">
<first>Jim</first> <last>Meadors</last>
</sig>
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And I lose interest and patience very quickly.
GCS d--(d+) s-/++ a C++++ U+++ P- L+@ E-- W++ N+ o+ K- w+++ O? M-- V? PS+ PE- Y+ PGP t+ 5? X R+++ tv-- b+(+++) DI+++ D++ G e++ h--- r+++ y+++* Weapons extension: ma- k++ F+2 X
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Same here.  
Everyone is born right handed. Only the strongest overcome it.
Fight for left-handed rights and hand equality.
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and I fear it was more luck than skill 
M.D.V. 
If something has a solution... Why do we have to worry about?. If it has no solution... For what reason do we have to worry about?
Help me to understand what I'm saying, and I'll explain it better to you
Rating helpful answers is nice, but saying thanks can be even nicer.
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It's impossible to solve the cube by luck. There are 43,252,003,274,489,856,000 possible states, every random move have a much higher chance to make it further from the solution then closer to it. If you were playing with the cube since the big bang you still wouldn't have even a remote chance of solving by now, with luck.
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Well, it doesn't mean every move had to be lucky! Perhaps he got it down to the last 2 or 3 pieces and then luckily hit the right moves.
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What are the chances of being born?[^]
but you are here, and so do I (luckily for us)
M.D.V.
If something has a solution... Why do we have to worry about?. If it has no solution... For what reason do we have to worry about?
Help me to understand what I'm saying, and I'll explain it better to you
Rating helpful answers is nice, but saying thanks can be even nicer.
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I can solve it by referring to a book (rather a booklet) I bought way back in 1987.
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I think I got the same. I memorized this universal algo when I was kid, with some practice I could solve it reliably under 1 minute.
However I yet to meet a person who can fully solve the cube without using a guide or algorithms. The first two layers are straight forward, but putting the corners in place on the 3rd layer is well beyond the capabilities of my spatial perception (without guide), and I guess its true for the vast majority of people.
So the real questions should be: Could you solve Rubic's Cube all by yourself?
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I spent the summer after it came out twisting it back and forth until I had learned enough combinations that I could always solve it. Then I heard about the 4x4x4 Rubik's Revenge and had to have it the day of release. And found that it could be solved by solving it down to something that matched the configuration of the 3x3x3 cube and then solving it as if it was a 3x3x3 cube. I have a 5x5x5 cube that is still in virgin un-elephanted state that I may never mess it up... 
<sig notetoself="think of a better signature">
<first>Jim</first> <last>Meadors</last>
</sig>
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The idea behind the cube is so simple but I have deepest respect for its creator.
There have been many clones out there, be it snakes, balls, all acting with the same principles, but... the cube is the cube.
This is true for the movies and this puzzle game
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