We sold our car when we moved to a different country. The only times I miss having a car are:
1. When the subway is so packed that I can't squish myself on three subways in a row. My solution is to now arrive at work at 7:45 AM so I am ahead of the rush hour crowd. Likewise when returning home from work. I leave an hour later (work longer days, but work fewer days each week).
2. When I have really heavy or bulky groceries, such as when I run out of oil, rice, diapers, and flour all at the same time, and have to lug them all home. I miss our car even more when I have to do so in the pouring rain. To address this, I order most heavy items online. Some of the grocery stores here provide free delivery. I may not be getting the best deal, but I try to save as much as possible by taking advantage of e-coupons. Plus, I do save the taxi fee home, so I guess it's a wash overall. Not throwing out my back and incurring several hundred dollars in medical fees is also a good thing.
3. Doing fun day trips is kind of a pain. I don't have a driver's license for the country in which I'm currently living, so day trips are limited to whatever is reachable by bus/subway. If I had a driver's license, I could easily rent a car for the day.
I do find it a bit harder to meet up with friends. I deal with this by not having friends...j/k. I find myself spending time with friends who live close by. It was one of the factors we considered when we moved to our new place. We actually chose to stay in our neighborhood and live a 5-minute walk from one of our friends, and a 10-minute walk from another friend, so we didn't have to make new friends. We see friends who live outside of our radius less frequently.
Other than that, it hasn't been more difficult, per se, just a different type of difficult. I don't have to worry about finding parking and paying for parking. I don't get stuck in traffic. I don't have to remember to bring my car in for tune-ups, renew the registration, etc.
As a caveat though, it's important to note that I live in a large, metropolitan city with a sprawling subway network and buses that come every 5 to 10 minutes, so having a car is not really necessary. I can get anywhere in the city (and even to the airport) within an hour using public transportation.
If I were living in an area with limited public transportation options, I would probably consider having a car even if I lived close to work. For example, when I lived in Vancouver, it would have taken me two hours to get to the airport, and going to church would have taken over an hour on Sundays because buses don't run as frequently. In that situation, even though I lived a half hour bike ride from work and a 15-minute bike ride from the grocery story (and frequently biked these shorter distances), we chose to keep our car so that our mobility wasn't limited.