Hi, long-time MMM reader here, new to the forum. I assume grocery delivery has been discussed a good bit on this forum, but I wanted to add my experience.
My wife and I have one car, so it's easy for us to drive to the grocery store every two or three weeks. (i know you're thinking we should be biking, etc. but trust me the route is not bike-friendly.) Anyway, we both have fairly stressful jobs, and our last several trips to walmart have been particularly unpleasant (long lines, crying/yelling children, products out of stock, etc.). So we finally decided to "pay for the convenience" of grocery delivery. (The service in our city is Peapod.) So we filled up our online cart and checked out, and it gave us options for when we would like our delivery to arrive. Some of these delivery windows are discounted, so if you're a bit flexible with your time and you're willing to order your groceries a couple days before you need them, you can get very low delivery fees. Our last delivery cost us less than $2 (how is this company surviving?!) plus we tipped the delivery guy $3. That's probably about the same cost as a drive to the grocery store - only instead of it taking almost two-hours and being stressful, it takes five or ten minutes in the comfort of our home.
So we're getting much more convenience at no extra cost. I only wish we'd known this when we moved here three years ago.
The only real downside is that the online selection is a bit smaller than the in-store selection for some reason. But if you're not picky, then it's not a big deal.
So for those of you with a local grocery delivery service, it's worth looking into their prices - it might be cheaper than you expect.