For groceries, I have 2 grocery stores along my commute path, so I drop in several times a week to pick up a few things. I find that more convenient (generally) than trying to do a big grocery run once a week. We rent a car once every couple of months for out-of-town trips, and usually try to do a big stock-up on groceries while we have the car as well.
I wouldn't bike to a social engagement unless it was very nearby (so I would be able to bike slowly and not get sweaty). I use public transit for that.
For me the big inconvenience is unforeseen trips, where we previously would have just hopped in the car. Yesterday my husband needed to rent a videocamera for work, and the rental place downtown (easily accessible by transit) wasn't answering their phone so he didn't know if they had it in stock. The one in suburbia had it for sure but would have been over 2 hours in one direction by transit to get to. So we rented a Zipcar, but the nearest one that was still available on such short notice was 3km away, and it was snowing and blowing. That certainly wasn't very convenient. Still better than if Zipcar wasn't around, of course!