Growing up we only had radishes raw. There was usually a bunch of them in a white bowl in water in the fridge. We ate them mostly with a sprinkle of salt. Sometimes they lent a spot of spicy color to a salad or crunch to a potato salad - a cold, refreshing crunch.
I've tried cooking up radishes and radish greens. No success so far with the greens. I just can't get past the scratchy feel of them which cooking them doesn't completely solve. (More shallots? Duck fat?) So far, the best luck I've had with radish greens is to scatter them about on a serving dish and then to place radish halves slathered with a watered down goat cheese spread on the halves atop them.
Cooking the radishes themselves, they lose their punch and become more like their turnip cousin. So I rarely cook radishes because they lose most of what I like about them. Last night I made a soup. I had decided a cold radish soup would be good. I googled and lo and behold found a recipe. It called for cooking up radishes, a leek and a shallot. I did (and ate several raw with salt while doing so). I added chicken stock, reduced it and then cooled it. Then the food processor for a rough puree. When it was time for supper I garnished it with radish slices and parsley. I'm pretty happy with it. It has taken its place in my limited cold soup repertoire joining gazpacho and cucumber. I need to make more cold soups.
The other thing about radishes I like is the blank stare I usually get when I talk about something having "had the radish." I've heard it has been used to refer to a person's being exhausted; though in my experience it was always about a thing, as in, this shirt has "had the radish," it's time for the rag bin. It's an expression I heard a lot growing up - my Dad's usually good for using it once every couple weeks or so. Not everyone is au courant though. I tried it out on my uncle who grew up in the same area last week. He didn't know what the heck I was talking about and he still lives in the Northeast Kingdom. Language is a funny thing. If you ever figure out where the origins of "had the radish," let me know. In the meantime, happy crunching.