Is it true that you should not exchange pieces when your down in material?

If so, what do you do? Wait for your opponent to make a mistake so you can catch up? (responsible chess strategy taking a blow here if I'm not mistaken....) Position your pawns and pieces to try and drive your opponents army back? I wouldn't like to say that I blunder all the time, but really, it happens, what do you do if you lost say, a knight, or a bishop? Is it all over? What I'd like to ask is: What should be your "strategy" when your down in material? I thought chess was, if more than anything, that it was all about tactics? I haven't played many games, my rating as of this writing, is 1412. Wheather I should be embarrassed, having a rating like that, and not thinking that tactics is more than just exchanging pieces............well I don't know the answer to that lol. Laugh if you have to but I consider myself still a beginner. Should your strategy be to continue exchanging and hoping that the middle or even all the way up to the endgame phase, that it will be in THAT phase, that some hope will arrive to get you back in gear? :) I think it's an important question, if you care for chess. We all blunder. Wheather big or small. Something happens in our games for the worse sometimes, when your opponent is in favor, so how do we all "reverse" that? Any thoughts?

exchange pawns, not pieces.

If you go into an endgame and they have an extra piece (or two knights!) it will be a draw.

The exception to every chess principles: unless it leads to mate!

I too am only in the high 1400s for live 30/0 chess... of course higher for online play, but I don't really count anyones online rating (essentially unlimited time, use of analysis boards and searchable opening databases all allowed, I mean come on! How does that help one's OTB play?) Anyway, if I go down a piece, I generally become suicidally aggressive and throw everything I have at trying to checkmate the enemy king ASAP, before he can trade down and take advantage of his extra piece.  I always keep an eye out for any tactics that will get my piece back, and if any of these tactics work out, then I will revert to normal play and try to win in the endgame, which I can usually do against other 1400-1500 players.

If you want to improve your chess and you lose a piece in an otherwise pretty equal position--you will resign.

You will learn more from playing another game than by trying to win or draw in a losing position.

I'm not so sure... isn't the ability to fight for a draw, perhaps even a win, conductive to improving one's chess?  Perhaps not against a grandmaster, but against most lowly mortals, weak moves and blunders abound... If I am a piece down, I take it as a challenge to play better, more tactical, more aggressive, chess than my opponent... It is amazing how many players will fold under the pressure... By resigning early, you are depriving yourself of an important chess lesson!

Yes.  Note that in chess lingo a piece is a non-pawn.

Naa, avoiding trades is just math.  The ratio gets much worse for you with each even trade.  e.g. 28 to 25 isn't as bad as 13 to 10. 

If you don't resign, and you don't attack, then yes, you're just waiting.

Well, objectively yes, against a peer a whole minor piece down for no compensation is dead lost.  The newer you are, the less it hurts your chances, but a non-pawn at any level is quite a bit.  Now if I had some compensation like an attack... (more below).

Generate activity / counter play in any way you can.  As longislandmark said you're not going to last in a long fight.  Win it quick or you're sure to lose.  Basically point all your pieces at something (like their king) as fast as you can (preferably most are already "pointed" heh) and make threats non stop.  If their position stabilizes (you no longer have the initiative i.e. can no longer generate threats that dictate the game) then you lose.

Experience shows that the easiest phase to convert a material advantage in is by far the endgame.  In fact if a player who is a piece down has failed to generate sufficient counter play in the middle game they usually just resign before the endgame even appears.

Tactics are usually short sequences of forcing moves that win material (or checkmate).  Basic tactic themes include pins, forks and skewers.  Exchanging pieces is just... well, exchanging.

One way to find counterplay is to make the position asymmetrical--e.g., having pawn majorities on different sides of the board, being castled on different sides, or having different minor pieces. Two bishops and a knight vs. two bishops probably will be easier for the stronger side than a bishop and knight vs. two knights. (That point will be relevant if you're in a fork and need to decide which piece to lose.)

Also, try to find moves that give your opponent a chance to make a mistake. Suppose you're considering two moves: one threatens a fork or back-rank mate, while the other is slightly better but threatens nothing, I'd play the first move, especially if the threat is easy to miss. (Or against a strong opponent, I'd probably simply resign!)

If there aren't many pieces on the board, you can play for a draw. Trading into a king vs. king and minor piece endgame (with no pawns) is the obvious way. Another way is trading into an endgame where your opponent has the wrong bishop (one that can't defend the square where his pawn would be promoted).

If you're down a pawn (or two) instead of a piece, trading into an endgame with opposite-colored bishops is a good way to draw.

You also can look for a draw by perpetual check, especially if the queens are still on the board.

Never give up your first 500 games, otherwise you'll never deeply understand HOW to win a game with an extra piece, because that's not always so easy. Let them prove it and be grateful for a free lesson.

"f so, what do you do? Wait for your opponent to make a mistake so you can catch up? (responsible chess strategy taking a blow here if I'm not mistaken....)"

Make it as complicated for your opponent as possible. Don't give him an easy win. Make the position double-edged. Then he/she is more prone to making a mistake. Of course, it will also be complicated for you too but that's what makes it fun!

When playing for a win, exchange pieces, not pawns.

When playing for a draw, exchange pawns, not peices.

Really?  Maybe for beginners it depends.  But realistically, I think it's time to resign if you're a piece down for nothing and you can't complicate things (or trade all the pawns off).

Yes for all the reasons people have mentioned. However there are a few exceptions, for example if you can leave your opponent with insufficient mating material or if it leaves you with a forced draw.

Sometimes I sac pieces for the attack. Just like Tal!

So very TRUE!!!!

There is a series on ICC which is all about trading pawns when behind in material. (It's actually about NOT trading pawns when ahead, but it shall work either way).

It depends, if your trading away pieces for postioning, future checkmates by all means trade, and even possibly sac if you have to

Is actually easier if you look at it the other way -- When you're ahead in material, Trade! Trade! Trade!!

Forget about attacking. Forget about pawn structure. Forget all that. Just simplify to a winning endgame, where your opponent will be helpless, without enough pieces left to hurt you.

Learn how to win while up material first. Then you know what to look for when down material.

K.I.S.S. -- Keep It Simple, Stupid.