I pickle everything. Onions & peppers, green beans, beets, and cukes. I prefer the sweet pickle brine to dill. I've not pickled asparagus, but that sounds interesting. I found an interesting recipe for dill asparagus pickles.
http://allrecipes.com/Recipe/Pickled-Asparagus/
Here's my grandmother's sweet pickle recipe...
http://www.hotwiredgardens.com/pdf/H...et_Pickles.pdf
They are my all time favorite.