The biggest single benefit for me is by far my freedom.
Cycling frees me from so many health problems that walking or driving would not. In fact currently I can't walk more than 200meters with crutches and only about 5m without (if that). I can't currently drive because of the lack of use of my right leg (I'm in the UK and you need to use the right leg for an emergency stop. to be honest I don't think I could actually hold the accelerator down long enough to worry about using the brakes but there we go!).
Cycling frees me from the rigours of daily life. It is a means to escape and be on my own with nature.
Cycling frees me from my disability. I may be slow and I am have to take my crutches with me, but few people even realise my bike has been modified to allow me to use it.
Cycling frees me from my asthma, my depression...
And most importantly right now, cycling frees me from my bed. I can't sit upright, so my only option is to lie down and that means I have been confined to my bed for the last 5 months (not kidding) and my recumbent trike frees me from that. It gives me an hour or so each day (6 days a week) where I can get outside away from the home because not being able to sit means I can't travel, can't leave the house, can't go shopping, can't go to the cinema, gym, swimming pool, shops...
Cycling is my freedom.