I remove mine. Depending on where you are storing your canned goods, the metal on metal can encourage corrosion. If I move them or make gifts out of them, I'll put the band back on for transport to ensure that they don't get bumped and break the seal.
I am fairly new to canning ...... do you all remove the bands from the jars after processing? Just wondering if there is a reason why some folks remove the bands and some do not when storing their jars after processing.