A lot of you guys say you roll up your straps. Although it was mentioned briefly in a response above, it is very important to do one thing because it cuts the amount of rolling way down. The ratchet has a fixed-length short ******** one end, and a long ******** the other end. Before you start rolling, pull the long strap so that both ends of it are the same length. Now when you roll it up you are doing the minimum amount of work.
I use blue painter's tape. It comes off easily, leaves no residue. I bring it along when I'm using the straps on a trailer. The loose ends I roll up and secure with blue masking tape. It's strong enough to hold, while being easily removed with no sticky goo left.
I have kept my ratcheting straps (and fabric hoist slings, same problem) in milk crates, which are light, strong and don't rust and let rainwater run through if accidentally left out in the weather. I keep one six footer loose in the back of my SUV which is fitted with 4 tiedown loops, factory. I use that strap ALL THE TIME.
I like the idea of storing them in drawers with partitions. I'm going to look into that.
metalmagpie