Furniture
Old wood furniture can often look like it needs to be replaced when really all it needs is a bit of TLC. Cabinet painting can restore a great piece to it's best again and bring new life to an old piece of furniture. Then there are upholstery shops where you can take a family heirloom, or a bargain you found at a garage sale and get it precisely to your taste. You can pick out the fabric and amount of cushioning and can have a piece unlike any other. If you think you'd be good at it, you can try reupholstering yourself as many people enjoy it as a hobby, and there are plenty of online tutorials that can help and inspire you.
Clothes
Some people just love shopping and want new clothes all the time, so even better if there's an excuse to and their clothes need repairing. Some clothes though, come attached with memories, stories, and feelings; there are things you just don't want to let go of even if they really have seen better days. Then there is just the matter of your wardrobe looking dated. If you're struggling with broken seams though, missing buttons, or an unraveling hem, then it's time to decide if it's worth repairing or replacing.
Cars
We all know that cars need maintenance and repair from time to time. Instead of buying a new car every couple of years, consider keeping your car longer. If you know your way around a motor, then you may be able to change batteries, oil, fan belts, spark plugs, and more by yourself, saving you a load of cash. Or if you know someone who can help you, perhaps you could do something in return for them. Or learn how to fix your car yourself, there are plenty of online tutorials to teach you. In terms of tires, think of tireworks.net for your needs there.
Appliances
When an appliance breaks under its warranty, fixing it is usually a no-brainer. But if it's out of warranty, then you need to consider the age of the appliance, the cost of a new device and how long either one is going to last you. You should repair if you think or feel that the appliance has a long life expectancy, but this varies for each different device and really is a judgment call. It's probably a good idea to replace though if your appliance is out of warranty and nearing the end of its life expectancy. Even if the replacement cost more than the repairs, it's likely at this stage that something else will go wrong with it, meaning that you will end up spending even more money.