I tend to repair everything, and let me say that's not true for the vast majority of my possessions, including cars, appliances, electronics, etc. It highly depends on the nature of the failure, but generally parts are cheaper than replacement. Here are a list of things I've recently repaired around my house + the parts to repair. I don't recall the parts costs, but all were far lower than replacing the entire thing:
Dishwasher: Control board
Garage door opener: Broken gear and sprocket
Hot tub: Two pumps and a pressure/flow sensor
AV receiver: Three capacitors
Rear projection TV: Convergence ICs
Attic fan: Fan motor
And probably tons more that I'm not recalling at the moment. The key is to stop throwing money away on labor costs. Even getting someone out to your house can cost $50-100 and that's before he even does anything. Total scam. I disagree with a lot of replies here--DIY repair is still a viable option for most things around the home.