1. Create a shopping list just for your kids. I did this for Hunter and he enjoys using it for about 10 minutes and then he's done. But, if your kids are older, and have longer attention spans, they will probably enjoy it more.
2. Give them each a small amount of money to buy a treat for themselves. Encourage them to weigh their options and pick the best deal (not just the first thing they see)
3. Make a grocery store scavenger hunt with a small prize for the person that finds everything first. (The items on the scavenger hunt list don't have to be items on your grocery list - make it tricky)
4. Have them talk to Grandma while you're walking through the store.
5. If your kids are little and still riding in the cart, go to the library first and pick out a new book that they can look at while shopping.
6. If your kids are older, make it into a competition. Divide the list in half and have a race to see who can finish first. Just make sure your list is very explicit so that the kids know exactly what you're looking for.
7. Play the alphabet game (like you do on road trips). Find labels that start with every letter, from A-Z. Have them work as a team, there will be less bickering that way.
8. Involve your kids in planning and cooking meals. When they have a say in what's going in the cart (and on the table), they'll be much more interested in shopping.
9. Involve your kids. Have them run the calculator. Ask them what flavors they want. Make one of them the list master and call out the next item on the list.
10. Take time to discuss nutrition as you go. As you grab something, talk about what food group is belongs in, what nutritional benefits it has etc.
There are probably many more great ideas out there, these are just a few to get you thinking. Keep changing things up - kids love new games and activities. When I am shopping by myself with the kids, I always go in the morning. The stores are slow and the checkers haven't been working very long. So everyone is a lot happier and more tolerant when it takes 5 minutes to unload the cart because my son insists on doing it himself. I also plan everything out before hand, that way I'm not standing in the aisle trying to decide what to get and trying to keep the kids happy too. Plus, when you plan everything out, you'll spend less time in the store, which is always helpful.
Remember that emotions are contagious. If you're not happy to be grocery shopping, your kids won't be happy either (and you'll be even unhappier because of it). If you decide to make it something fun, it will be. There will always be highs and lows (as always), but you can maximize the highs and minimize the lows.