So, you have a concrete patio or a driveway that is cracked and damaged. Should you repair or replace? Repairing is cheaper in the short term - but is it worth it in the long term?
The answer is, of course. The key factor is whether the concrete has "settled" on either side of the crack. If it has, this means the concrete is cracked all the way through, and any repair will not last long. Concrete that has either sunk into a pit or risen into a mound is also often not worth repairing. The latter, called "frost heave" is very common in colder climates. All of these tend to be signs that the job was not done right in the first place - it is very important to hire a good contractor and get a good pour. It is also important to use the correct subgrade for your climate and conditions.
Hairline surface breaks, on the other hand, are a simple repair - in some cases, they can just be filled with cement and water, although if you are in doubt, you should always call a contractor.
Spot replacement or patching is also a cheaper option, although it will never look quite the same as the original, and eventually, a new pour will be required. Ask your contractor whether spot replacement will last long enough to be worth it, and consider whether the obvious damage will have an effect on the look of your home and yard. Also, make sure that if you do do a new pour that the subgrade is correct and properly prepared - or you will have the same problem again in the not too distant future.
Knowing whether to repair or replace can require a certain amount of skill - if in doubt, call a qualified contractor for a professional opinion.