Had this discussion recently with a few friends. We all are growing basil in our gardens. One told me she just cuts almost an entire plant at the base, sticks it in a paper bag, and puts the whole thing in the freezer. I tried this and the entire plant turned black.
Another friend says she picks all the leaves off and puts them in a plastic bag; sticks the plastic bag in the freezer. Again, basil turned black and mushy for me when I have tried that.
The only way I have successfully frozen basil and had it stay green is by doing the following (another friend taught me this):
Pick leaves, and chop.Toss with small amount of salt and some olive oil. Place basil and olive oil mixture on good quality plastic wrap; mold it into a long, thin shape (like a cigar)
Roll plastic wrap tightly around basil 'cigar', and then cover the roll with tin foil. Store in freezer.
As you need basil, remove the tin foil and peel back the plastic. Chop off as much as you need, and re-wrap carefully before putting back in freezer (do not allow to defrost)
Basil always stays green and does not loose flavor this way.
I'd like to see what others do to store this herb.