Jumps will have impact on your knees, as will running for extended periods of time. However, squats past parallel actually make your knees stronger. The reason for this has to do with muscle balance. The most common risk with exercise, is focusing too much on what you like without doing what's necessary for what you don't like to do. Core exercises are a common class of exercise that get dropped because they are not fun.
You have several muscles in your legs, and with most activities the anterior (front side) muscles get exercised much more than the posterior (back side) muscles. When you consider that the anterior is what we see when we look in a mirror this makes sense. For some information about the kenisiology of squats check out this exrx.net article.
Proper squats to depth exercise the following muscles:
- gluteus muscles
- core (both back and front)
- and if loaded with dumbbells, kettlebells, or barbells--your arms.
It truly is a full body exercise. Any replacement would have to address all these areas. Back extensions will hit your core, gluteus and hamstrings, but won't do much for your calves. The quadriceps get more than enough attention through other exercises (like running, cycling, etc).
The next closest useful relative of the squat would be the lunge. But it is inferior to the squat--particularly if knee health is a concern.