The Every Skill Ever System

Note: This is probably going to work best in d20 basic d&d type systems.

Giving a PC in any system a stat/skill/ability/feat not only defines what that PC can do, but defines what they can't do.

In a highly granular skill/feat based system this can lead to silliness; a character missing the art skill couldn't ever draw a picture, a character without the etiquette skill couldn't ever talk his way in or out of a situation, a character without shield-bash couldn't possibly ever hit something with his shield.

The 6 attribute system (strength, dexterity, constitution, intelligence, wisdom and charisma) defines in an abstract and vague way what a character can do. It also defines what he can't do and how well he can or can't do things in general.  The 6 attributes essentially correlate to the experience of being a human being on earth. It's not a system for roleplaying a psychic-inter-dimensional-gas-blob, a time traveling flat man or human being NOT chained to the constraints of physical reality on earth. It's also not relevant to roleplaying a duck, amoeba or other non-human carbon based life.

Anything a human being could do can be extrapolated into a roll from these 6 attributes.

The reason for having a stat/skill/ability/feat is to calculate the bonus to a chance that a character has of achieving something of consequence. There's no reasons to roll for entering a shop but there could be reason for rolling to enter a shop without any one seeing you.

Players should want to do things all the time, all types of different and varied things.

Let them do things; simple relate the thing they want to do to the most applicable attribute and get the player to attempt a  D20 roll under their listed score for that attribute. This is colloquially known as an Attribute Check. This is the basis for the Every Skill Ever System.

Only do this when the thing the player wants to do is something that will have a consequence for either attempting it, achieving it or failing it.

Apply bonuses and negatives to each roll when relevant. This is the important part of the Every Skill Ever System. As the player is trying to roll the lowest number possible on a D20 (to get a result under the relevant attribute score) a bonus would be a subtraction from the roll result and a negative would be an addition to the roll result.

It's going to be easier to enter that shop unnoticed when it's dark, crowded and the character is wearing a hood (that sounds like a -2 bonus to the roll result to me).

It's going to be harder to enter that shop unnoticed when the character is wearing a clown suit and narrating his actions in a shouted voice to the people around him (+4 negative to the roll result).

Communicating to players that proper preparation and intelligent description of how they want to attempt a task will convey a bonus or a negative gives a great space for roleplaying. 

It's important that as the 6 attribute system correlates to the experience of being a human being on earth, players can't do things that human's can't do. No flying on a passed strength check.

It's also important to remember that just like here on earth some things are hard, sometimes impossibly so (this sounds like a +20 negative on the rolled result to me). I can attempt to pick up a car, but its not going to happen. Plus when I do this there is a chance I will injure my back or look like a fool (remember to only roll when there is a consequence for attempting, achieving or falling a roll).

Because it's a game, allowing criticals (a natural 1 in this case) to succeed on seemingly impossible tasks results in some loveable over-the-top action. Ensure there is negative consequences for failing though.

One final caveat of the Every Skill Ever System is that it works best for tasks attempted "in the field". Tasks that can be boiled down to a singular, or a small number of actions. Long term tasks (scientific research, writing a book) require a bit of extra work for the DM in the application of consequences.

Is learning or remembering how to play a piano related to intelligence, wisdom or dexterity?

In reality it's probably a combination of the three, but in a game it's up to the GM. It's important that once a call is made, it's written down and remembered to avoid discrepancies in further piano playing checks.

Is it important to write down every skill human beings could do ever and relate them each attribute? 

No, in fact just by writing that list down your putting boundaries on what players can attempt to do in your game. Define skills to attributes as they come up, don't waste time thinking up what players might want to do.

What about player's that want their characters to get better at doing a certain thing over time? 

Let them do it. But as every human being on earth is aware there is consequences for everything you do. The onus is on the GM to make sure this principle is applied logically to 6 attribute system (along with any of the other player resources included in the game).

If a character wants to get really good at playing the piano (say, receiving a -4 bonus every time they attempt to perform) there going have to spend time and money. Also, those months spent practicing the piano they would not have been working out in the dungeon (taking a hit to their strength or constitution).

The Every Skill Ever system recommends never, ever giving character's bonuses to attributes from levels or miscellaneous magic items.