Not knowing your age, fitness level and type of amputation, I'll just recommend you some exercises that don't really depend on those factors.
As a swimmer with relatively poor leg technique I can assure you, you can swim perfectly fine without legs. Technically speaking you should even float easier, due to the reduced average density of your body, so if you know how to swim, you should be pretty safe. Furthermore, you can get swimming aids which should even allow you to scuba dive.
Either way, swimming is a great exercise for both the core, your lungs and your arms. Obviously the arm training should benefit you when you go walking with crutches and any other situation where you use your arm to support yourself. Sticking with freestyle and backstroke is probably the safest, though I have no experience with how well turning goes, but I'm sure you'll manage.
Granted, you'd have to buy a special bike for it, but it does make your more mobile. Rather than having to take the car everywhere (grocery shopping etc) you could take the hand bike instead.
Again, its a great arm exercise, you can vary the intensity of your workouts and since your sitting, its much easier to keep it up for longer stretches. Compare that to going on a long hike and getting tired on the way back...
You should still be able to do most weight lifting exercises. Either go to the gym or buy a set of weights so you can do them at home. You can also perform one-legged quads, though I suspect your leg already get's plenty of exercise during the day. Unless your physician recommends it, I'd stick to arm exercises and train your leg by walking instead.
While cardio is important for staying fit, I'd also recommend to regularly do some yoga. Not only does this keep your hip/knee joints flexible, which should help you stay mobile. Training your balance should help you make up for the lack of stability and reduce your injury rate.
Above all else, cherish your leg, so don't overdo any exercise, because that would truly make you immobile. Luckily all of the exercises I recommended can be done without your legs, so you can choose for yourself whether you want to use them or not.
Good luck and be sure to come back if you have any more specific questions!