Heart testing can tip you off to serious conditions that you can attempt to treat with medication. That would be a Doppler echocardiogram to detect flow rate problems (especially if the dog has a murmur). Some heart conditions are relatively benign for the individual -- things that would prevent you from breeding that individual animal, but are unlikely to require medication or shorten or alter the dog's natural life in any way (mild aortic stenosis). Others may not require treatment now but would bear watching year to year to see if they progress and start causing problems.
If the dog has arrhythmias (detected on a 24 hour electrocardiogram, also called a Holter monitor) there are medications that will reduce the number of arrhythmias (and fainting spells if the dog starts having them) but there's no real evidence that they prolong life. Absence of arrhythmias on the test DOES NOT mean that the dog is clear, but the test will often pick up really bad cases, and then you might consider medication and have something of an expectation that the dog might not live to old age.
Thyroid conditions are quite common in boxers, so a thyroid panel could tip you off early to very treatable conditions.
Hip testing could alert you to potential problems in the future with arthritis and should certainly be done if your dog is quite active, especially in agility or jumping or jogging -- a dog with bad hips who engages in intense exercise can be creating further injury down the road.
In short, it's up to you. Breeders use the tests to weed out the worst cases before they pass on the conditions to the next generation. Ignorance isn't a luxury the ethical can afford.
If you're not breeding your dog, much will depend on why you want the information. Are you the type who will obsess over a "not so good" report that won't necessarily (but might possibly) shorten your dog's lifespan? Or would you rather know sooner than later that there's the possibility of a bad outcome?
If the dog has a murmur I'd definitely do the echo, because there are medications that prolong life and prevent other complications from certain structural disorders. I might do the Holter if I was curious, but you have to understand that there's no clean bill of health from it. The only reliable information you can get is bad -- that the dog has an extremely bad electrical system in his heart. A good report just means that it didn't detect any that particular day.
