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Solid rule-of-thumb principles off the top of your head

-- Pieces are strongest on the board
-- Always play check, it could be mate
-- When in doubt, move a knight
-- Bishops are stuck on one color
-- Two rooks are better than one
-- If you're ahead on the clock, play for complications. If you're hungry for lunch, offer a draw.
-- Once moved a pawn can never move backward
-- It takes two to Tango

-blockade isolated queen pawns with pieces, preferably knights
-rooks belong on open files
-knight on the rim = dim, hence, chances are slim
-castle before starting an attack

Remember these are rules of thumb, there are exceptions!
Off the top of my head:
Brink your king to the middle of the board asap in an endgame.
Develop quickly and to control the center in the opening.
Castle to the side where your pawns have not moved.
Castle before opening lines or if lines are about to be opened.
Seek play where your pawn chain "points" (where you have more space).
Mobility (or prospective mobility) of a piece is often it's value.
In closed positions find your worst placed piece and improve it.
Just like the opening, in the middle game it pays to have your pieces coordinated before opening lines (pawn breaks) or if your opponent is about to.
Ignore your opponant's threat if you can.
Passed pawns much be pushed.
Passed pawns must be blockaded.
In the endgame rooks belong behind passed pawns for either attack or defense.
In rook endgames worry about your rook's activity, king's activity, and preserving your pawns in that order. e.g. rook's activity and king's activity is worth giving up a pawn.
Passive defense in an endgame should only be used as last resort. If you don't have a fortress it's as bad as resigning.
Knight endgames are like pawn endgames, a small advantage can mean victory or defeat.
Knight endgames are like pawn endgames, lots of calculation is required.
In queen endgames place your queen in the center of the board, preferably in contact with your weak pawns.
In queen endgames an open king means a perpetual is available.
Passers are very strong in queen endgames as the queen is the only piece able to escort the pawn to the other side by herself.
Open lines / Attack where your opponent has less power. This can be due to less chessmen, less space, disorganization (development), vulnerable king, or because of weak squares/targets.
Two pawns on the 6th rank beat a rook.
A pawn on the 7th and a pawn on the 5 also beat a rook.
Rooks belong on the 7th.
A knight on the 5th is greater than a bishop, on the 6th greater than a rook.
In the opening a tempo is worth 1/3rd of a pawn.
Regarding pawns, capture towards the center.
Regarding pawns, capture to keep fewest pawn islands.
Attack a pawn chain at it's base.
The pieces are your army, the pawns are the terrain.
In the middle game pawns are best abreast (complimentary attacks and flexible for either to move forward).
Blockade a passer and then destroy it.
IQP position if you have the pawn you want activity and initiative. To play against it blockade it and trades lead to a favorable endgame
In endgames pawns on their original square give you an edge in tempo battles.
In endgames when pawns attack each other leave the tension unless by exchanging you'll gain an advantage or avoid a weakness.
In endgames notice your weak pawns or base pawns. If on the 2nd rank your position is solid.
Picking up a center pawn points towards the correctness of an exchange sac.
Zugzwang is to endgames as tactics are to the middle game.
Knights need outposts.
To fight a knight take away it's squares.
As an attacking duo a queen and knight are better than a queen and bishop.
Concerning batteries place your queen in front of a bishop but behind a rook.
Place your pawns on the opposite color of your bishop.
If your opponent has lost his light square bishop strive to make yours more valuable by placing pawns on dark squares.
To cure a bad bishop trade it, activate it, or move your pawns off it's color.
Rooks become more valuable as pawns come off (more open files to operate)
Two rooks on an open board are often better than a queen. (so R+R > Q in endgame R+R < Q in middlegame)
Keep your rooks on the back rank until the endgame.
Rooks belong on open files.
In the endgame the king is a fighting piece whose activity is worth more than a minor piece but less than a rook.
Trade pawns not pieces if you're behind.
Trade pieces not pawns if you're ahead.
Avoid trades if you're ahead on the clock, ahead on the board, or higher rated.
For tons you can go here:
http://danheisman.home.comcast.net/~danheisman/Articles/Dan_sayings.html

Remember these are rules of thumb, there are exceptions!
Off the top of my head:
Brink your king to the middle of the board asap in an endgame.
I think you mean in the opening.

Rooks belong behind passed pawns, whether they be yours or your opponents.
A rook on the 7th (or 2nd in black's case) is worth a pawn.

-- If you're ahead on the clock, play for complications. If you're hungry for lunch, offer a draw.
It's the golden rule.

A rook on the 7th is worth a pawn.
A pawn on the 7th is worth a rook!
Which seems to enter us into some kind of infinite loop.

TAKE YOUR TIME! It only takes one bad move to lose a game. So be careful on every move!
Before you move, look for any captures you can make, can you put your opponent in check? Will the piece you want to move be safe? Now ask those same questions about your opponent’s pieces. After you do that – then pick your best move.
Playing chess is like a series of puzzles, move after move, where you have to take your time and solve the puzzle: 'What is the best move?
When in doubt, find your least active piece and make it active. Every piece can help your army win.
Every move should be helping make you stronger.
Don’t make to many Pawn moves starting out a game, just make enough to get your pieces into battle.
For the first 8-10 moves, try not to move any piece twice (unless you have to). Instead, move each piece once to get it into position.
Get your Knights and Bishops out earliest, and then castle. Don’t bring the Queen out too early – she can get trapped if the board is too crowded.
Don’t start your attack until your pieces are all out on the field and ready and your King is safe.
In chess, the attacker wins. Defenders win only when the attacker makes a mistake. Even then, the defender must become the attacker to win.
Castling is ALWAYS a good move.
(letting the Wookie win is always good advice)

Take the queen, mate him later.
Or my favorite:
The square of the opposite colored bishop belongs behind the passed pawn
( roughly translated => don't muddle up your head with too many thumb rules/guidelines all at once :) )

Castling is ALWAYS a good move.
Certainly not. Castling is usually a good move, would be better advice.

Option Principle: "The Option Principle states: make the move (develop the piece) which does the least to reduce your options to make other important moves. When there are several pieces that can be developed, move the one for which the Optimal Placement is most clear. This is a generalization of Lasker’s rule ‘knights before bishops’." (Berliner, The System, p.36-37) Weaver Adams' original formulation of the Option Principle can be found here: http://oeco.blogspot.com/2010/12/option-principle.html
I've got a new student & wanted to give him a big list of general principles (which I could hopefully then illustrate as they came up in games we analyzed.
The more the merrier, shoot!