What are all the factors that influence the guitar's sound (not counting pedals, amps or the player) and how much do each factor influence the sound? Eg. The pick-ups, the wood, the strings, the shape (?), etc.
You can't break it down into percentages, it doesn't work like that. There are a lot of things that factor into tone and how much a factor they are depends on the particular guitar.
My name is Tom, feel free to use it.
the other electronics like Pots, wiring, jack and capacitors has a huge impact. Case in point Jimmy page's wiring upgrade for les paul guitars.

Also how close the pickups are to the strings, and action affect sound. Closer the pickups the hotter the sound.

Gauge of strings, woods, type of bridge, nut, etc Type of pick you use

But in all honesty the biggest thing is your amp. With an awesome amp you can make a very shitty guitar sound awesome.

Playing with your eq settings has a huge impact.

I'd change things in the following order
1, Buy the best amp you can afford for what you need to do
2. rewire your guitar
3. Change pickups
4. Buy pedals
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Last edited by reggaebassman at Sep 7, 2011,
Guitar----amp-----operator. You pick the order and how much each effect sound/tone

The following statement is true. The proceeding statement is false.
The amp.
- Whether it's ss or tube. If it's tube, the tubes will affect the sound. The quality of the wire/ components in the amp, what speaker cables you use if it's a stack.

- No need to explain this. I guess true bypass or not will affect it and low batteries, if you use them.

The guitar.
- Pickups obviously. EMG's will obviously have a different sound to passives.

- The wood. Mahogany generall has more warmth and bass than say Ash. The amount of wood that makes the guitar. How the neck is joined. The quality and age of the wood. The finish, to a certain extent. There's a lot of debate about different paints.
The humidity in which the wood was grown in/ stored.

Everything involved will affect the sound. Two of the exact same guitars probably will not sound the same. When looking for my Gibson Les Paul, I tried out loads. The guy in the shop gave me two identical guitars. Make, model, colour, everything was the same. However, one was a lot heavier than the other.
I'm going to close this thread. It's far too broad, like asking "what tastes good?" You're going to get a million posts like the "this many percent!" one, which are, frankly, completely stupid. You've gotten some decent answers so far, but that's about as much as can be said - there are two answers to your question.
1. Nearly everything influences guitar sound. Your straplocks, maybe not, but nearly anything in your signal chain and many things peripheral to it.
2. There is no way to say "how much" something effects the tone. There is no control group for guitars, there's no "regular" guitar, there's no way to compare all guitars against all other ones, so asking how variables work across such vastly different instruments is a seriously misguided question. The only way to "answer" it is to experience and understand the workings of instruments.