As well as the obvious benefits of a motor (i.e helping you get up the hills more easily and with less sweat) there are other benefits that might not have occurred to you...
They can make a hilly or long commute more manageable, get you further afield on leisure rides, or restore a lapsed love for cycling.
They can be a viable replacement for a second car with all the environmental, financial and other benefits that this entails.
As an e-bike you can carry heavier loads more easily than with a regular bike, many shopping trips or the school run might now be a possibility.
E-bike riders often say they feel safer in traffic than when riding a non-powered bike, as the extra acceleration and speed up hills mean the speed of other passing vehicles is less than it otherwise would be.
If you have an injury or illness, e-bikes may enable you to keep pedalling through it, rather than giving up cycling completely.
It's not cheating! You still get exercise. Any time you go out on a bike, e-bike or not, your heart rate will go up. Most e-bikes have power level settings on the handlebar controls that let you dial down the power if you want more exercise, or turn it up if you need more assistance.
they're just great fun to ride