At risk of sounding melodramatic, I think my life would have been worse.
For one thing, it would mean I would only really have one hobby instead of two, which would be a shame.
I would also have been far, far less fit. It's possible I might have played another sport, but I doubt it. I was the kid with far less ability in just about all sports - I'm dyspraxic, and was embarrassingly bad at just about anything that required coordination. I didn't hate sports, but I didn't enjoy them until I began running . An unexpected side effect of running has been to make me far, far better at almost every other sport (combined with my coordination still being below average, but significantly improving). This is a big confidence boost - I can run rings around people on the soccer field now, simply because they are less fit than me. I love the feeling of being fit, and if it wasn't for running, I think I'd be a feeble, uncoordinated specimen now. I might not have been overweight - I've always been fairly disciplined - but I wouldn't be healthy.
I also might not have been so close to my Dad. We would still undoubtedly have been friends - he's who I look up to, and he's hilarious - but we first had a real interest in common when he began running with me at age 11. We still talk about running all the time, only it's rowing for him now due to injury. As a digression, I think it would never had occurred for me to run if he wasn't a runner, so for me, this question could just as easily be "what if your dad wasn't a runner?" rather than "what if you had never ran?" I treasure this common interest, and if I ever have children, I will take them running with me.
This is perhaps more nebulous, but I think I might not have achieved the academic results, and other results, I have without the grinding mentality running gave me. Running is also just about the best way to shake off the shackles of work - there's something about running after work to clear your head, instead of simply sitting and doing something else.
Running changed my life for the better. I love it, and, injury permitting, I know it will be a lifelong hobby. Great question.
Signed - an 18:29 jogger looking to run a lot and keep enjoying the ride.