I find doing Chess Mentor is excellent for making me consider all these issues. Still a long way to go though
What are the common "non-blunder" mistakes non-beginners make?

#8 I like a lot. It's weird, I'll see a game, pretty close for a long time. Then one of the players goes up a rook or something. And he keeps thinking about his moves the same amount of time, as though he doesn't realize he's up a rook. And then, as you say, refuses to exchange when the position is really screaming for it. If you're up a whole rook, then getting queens off the board is worth doubling pawns. Heck, it's even worth losing a pawn in the deal, probably.

I like #3, don't trade simply because you can, make sure you still like your move even if they ignore it type of advice.
These are all good, maybe I can think of another -- it's not worth winning a pawn or two if you let an enemy rook/queen infiltrate, especially a rook on the 7th or getting the absolute 7th... or something similar like don't be blinded by winning a few points of material at the cost of your position. Maybe something like exchanging off your best minor piece even if it's for a rook, maybe all pawns around your king are on light squares and they still have dark square bishop, so you think twice to trade it for a knight, even if you win a pawn out of it etc.

I think most people lose because they are to Lazy.
They believe a split second analysis or shortening their thought process (not blunderchecking or looking what an opponent attacked) is good enough. For Pete's sake! Tie on a pair and get the job done.
If you decided to set down and play a game then pour your heart into it. Most people dont lose because a lack of head knowledge or something that is not forseeable... buckle down and do the work.
If you are a person that is okay with a half-hearted play then you have no right to complain about it.
-amature

Allowing your queen to get trapped in a passive position. I know you shouldn't bring your queen out too early because she becomes a target. However, having your queen on the side of the board away from the action is nearly as bad.

Being too afraid of having any kind of pawn weaknesses. When I first started I would go crazy making sure I never had isolated, doubled, or backwards pawns. Now I realize that the tempi i was spending keeping my pawn structure intact could have been used much more effectively. For example allowing doubled pawns but being able to get the initiative, or the 2 bishops, ect.

3. Make unnecessary or knee-jerk trades and hope something good happens after that. If you look at the games of strong players, you'll NEVER see this behavior. Maintaining "tension" and the famous "the threat is always better than the execution" are mantras they follow well.
4. Play h3/h6 or a3/a6 when the position does NOT REQUIRE IT and rationalize it as luft for an endgame. Well, experience has taught me that by weakening a kingside in this manner against a stronger player, you probably won't really get to an endgame.
8. NOT simplify material when you are winning or even worse => simplify material when you are losing.
9. (Update) : Defending an attacked piece with another piece, usually of higher value when complications can be avoided by moving the attacked piece to begin with.
Wow. What a great thread topic. No. 3 and No. 8 I have serious problems with...I need to save the list.
lol..."hope something good happens after that".

My cat always brings his Queen out too soon-- I can't break him of the habit. You know how cats are . . . attack, attack, and when in doubt, attack. On the other hand, he plays a heckuva Benko Gambit . . .
--Cystem

6. Attack when the position does not favor it. This includes your sophisticated school-kid "Bc4 + Qh5 + mate the bastard" idea as well as making threats (checking for the sake of checking for e.g.) that really help your opponent more than it helped you.
Yes. However obvious it may seem a lot of players don't seem to realize they can only attack when they have the advantage (except in one of those balanced opposite sides castling positions of course).
Really common I've found is when playing a weaker player in a pawn up Endgame they'll just throw forward their pawns on the same side which my pawn majority is and make it easy for me to get another passed pawn/create extra weaknesses. I had a game at the weekend which went this way:

7. Opposite of 6. Not consider a flank-attack with pawns when the position is SCREAMING for it. This still remains one of my personal vices. :)
Could you give an example to this? When do we understand when a position SCREAMS for a flank attack?
My addition to the list would be
-bringing the rooks to the game too late.
-being too scared of doubled pawns.
-absolutely hating queen trades and trying to avoid them at all costs.

The typical example of a flank attack is when the center is closed, no? Like in the French Advance or the King's Indian.

7. Opposite of 6. Not consider a flank-attack with pawns when the position is SCREAMING for it. This still remains one of my personal vices. :)
Could you give an example to this? When do we understand when a position SCREAMS for a flank attack?

IM Silman, in his book "The Amateur's Mind: Turning Chess Misconceptions Into Chess Mastery", gives a couple of generalizations that I like:
Don't forget that your opponent also has a plan
but at the same time
Don't "react to ghosts" (fear every threat your opponent can make)

Top thread !
I suggest : "Turn into a complicated game when being up material"
Right, this is exactly what your opponent wants when they're down. Every piece exchange is one fewer piece that your opponent can attack with. It also saps the energy out of them. The theory is that because you can propose exchanges and they are basically forced to decline them, you can "easily improve your position" and then win.

Mark me as one of those who worries about doubling his pawns. But I think my history gives me a right to worry-- it almost always gets me in trouble. Conversely, I tend to assume everyone else hates it too, so I tend to push things like Bishop-Knight exchanges where my opponent has to do his recapture with a pawn and ends up doubled. That's one reason I like the Nimzo-Indian-- I love the ...Bxc3 bxc3 Bishop-Knight exchange!
--Cystem
Based on a forum thread from a while ago, thought I'd repaste what I wrote and now hope to collect a lot more observations from strong players.
Beyond the obvious tactical mistakes that plague most non-beginners, I'd listed out my own observations of "thinking errors" that I encountered across the board as well as the ones I made often during my first 30-50 tourney/OTB chess games.
1. Play break moves with pawns without any long-term thinking about what may happen after the break. The most common "defective" thoughts are assuming that your opponent will instantly trade pawns and not ignore you or walk his pawn past yours.
2. Move a piece more than once if you haven't finished your development. You really should only do this if there is a tactical need for it.
3. Make unnecessary or knee-jerk trades and hope something good happens after that. If you look at the games of strong players, you'll NEVER see this behavior. Maintaining "tension" and the famous "the threat is always better than the execution" are mantras they follow well.
4. Play h3/h6 or a3/a6 when the position does NOT REQUIRE IT and rationalize it as luft for an endgame. Well, experience has taught me that by weakening a kingside in this manner against a stronger player, you probably won't really get to an endgame.
5. Create holes in your position with pawn-moves, especially when you feel you are being squeezed.
6. Attack when the position does not favor it. This includes your sophisticated school-kid "Bc4 + Qh5 + mate the bastard" idea as well as making threats (checking for the sake of checking for e.g.) that really help your opponent more than it helped you.
7. Opposite of 6. Not consider a flank-attack with pawns when the position is SCREAMING for it. This still remains one of my personal vices. :)
8. NOT simplify material when you are winning or even worse => simplify material when you are losing.
9. (Update) : Defending an attacked piece with another piece, usually of higher value when complications can be avoided by moving the attacked piece to begin with.
Any more ... ? Please list out only non-tactical mistakes. Poor tactical strength can be cured but the list of bad "chess habits" I'm trying to compile tend to stick no matter how many puzzles you solve each day.
Thanks in advance!
Further Update (2/27/2010):
( PHENOMENAL response so far ... thought I'd add them to the list and give credit to those who posted them in.)
10. trading away a bishop pair without a good reason(eaglex)
11. Allowing for the doubling of pawns or isolation of pawns without resistance. (checkersgosu)
12. Getting material-greedy leading to positional disasters. e.g. Allowing 7th rank rook infiltration for a pawn. (orangehonda)
13. Exchanging your best minor piece when it is not required.(e.g. a fianchetto bishop when the opponent still has one of the same color) (orange honda)
14. Allowing your queen to get trapped/inactive (brianb42)
15. Too afraid of pawn weaknesses (double/isolated/backwards) when they really aren't so bad. (cubbie, philidor_position)
16. Pushing pawns in desperation and creating new weaknesses in endgame (Nuclearturkey)
17. Bringing rooks in too late (philidor_position)
18. Avoiding Queen Trades (for no darn reason!) (philidor_position)
19. Bringing the Queen out too early. (csystem_phailure)
20. Forgetting your opponent has a plan (Silman via Sigmoid_Flexure)
21. Reacting to ghosts/threat-like moves that really aren't threats. (Silman via Sigmoid_Flexure)
22. Knee-jerk Castling when you really don't have to. (rrrtt)
23. Overcautious. Spending too many moves to prepare an attack (jonnyjupiter)
24. Making/Executing plans on the wrong side of the board.
(jonnyjupiter)
25. Getting into time-trouble ( costelus, theGrobe, jonnyjupiter, philidor_position)
26. Assuming your opponent will NOT find the best response ( theGrobe,Spiffe)
27. Not trusting instincts. Over-analyzing/re-checking/wasting time. (jonnyjupiter)
28. Castling into it (from the frying pan into the fire) : philidor_position
29. Not developing rooks fast enough (smileative)
30. Under-analyzing/lazy armchair analysis of critical positions: khpa21
31. Under/Overestimating opponent based on rating : ReedRichards
32. Being too content with developing to good squares as opposed to effective squares. (nuclear turkey)
33.Playing without a plan (bodiggity)
34. Not recognizing imbalances or doing anything about them (bondiggity)
35. Underestimating your opponent based on their age. (chessowns)
36. Overvaluing checks without calculating real consequences (orangehonda)