Since we keep worm bins in our basement, we save most of our kitchen waste (except meat and dairy) for them. The majority of it goes directly into a huge container that we keep in the fridge until feeding time, but I prefer to do the eggshells differently. It works so much better if I dry them first (which means nothing more than leaving them in their containers and sticking them in the garage) and then crushing them at a later date.
And even if you don't do any type of composting, this might still be a good project for you. Just sprinkle the crushed shells directly around your garden. The calcium they contain is especially helpful for fighting blossom end rot in tomatoes.
Sometimes I crush them with a little flat mallet thingy and other times I toss them in the food processor.
I hadn't done this in a really long time, and recently decided that I ought to, after my life was imperiled by a toppling tower of saved egg cartons.
In case you don't want to count, that's 29 dozen eggs.
This is what it's like to live with the crazy that is me.
Note- I did eventually get around to reusing some of these cartons like Green Bean challenged me in the comments.
Worm Composting (1)- Setting Up the Bed
Worm Composting (2)- Some Other Thoughts
Worm Composting (3)- Harvesting The Castings
Worm Composting (4)- Troubleshooting
Why You Need Worm Poo