I'm often asked if it is worth having a piece of furniture repaired. The answer to that is, “it depends”. If a piece is well built, needs minor repair or has sentimental value, the answer is yes. As a rule I don't recommend repairing pieces made of particle board. It's often cheaper to replace them, and these pieces generally have structural issues as well.
Lets look at each of these categories, starting with a well built piece. What constitutes well built? Solid wood construction or furniture grade plywood with sound veneer is a good start. Traditional joinery such as mortise and tenon or dovetails all add to a pieces integrity. While these are some good indications of quality furniture, they are by no means the only ones.
Any piece that needs minor repair should be considered for repair. Small scratches, dents or stains can usually be easily repaired. Even chips or damaged doors or drawers can be quickly repaired. These small repairs can be done so the entire piece won't have to be refinished. Even if a table top needs to be stripped the legs, aprons and supporting structures can usually be left as is, thus saving time and money. Even pieces that have dated or worn fabric can easily be re-upholstered and give a “tired” chair a new life.
Items with sentimental value should always be considered for repair. You can't replace your grandmother's hope chest or your dad's shoe shine kit. Things like that are too important to us and if they can be brought back to a like new condition for a reasonable sum, then do so. Not only will it be around for years to come, but if it's in good condition you're more likely to display it and remember all that it has come to mean.
While I have done repairs on lower quality (particle board) pieces, I usually discourage people from this. Most of these pieces are assembled with inadequate joinery, poor materials and are covered with a picture of wood. These materials don't take fasteners well and can't be refinished. Scratches, dents and dings are all permanent and the only way to fix them is to veneer the entire damaged area. It's best to replace the damaged area (top, shelf, side, etc), or the entire piece. Items like this are disposable and I suggest they be replaced with something better built.
So is the piece worth repairing? That's really up to you. I've brought back a lot of items that others said couldn't be fixed, and at a reasonable price. Other pieces I turn down because it's just too far gone or not worth the cost. The question is how much do you want the piece and is the price for the repair reasonable to you. Speak with a woodworker you trust and get their input. Given the choice, I'd rather repair an item than toss it, but it has to be sound to begin with.