I found a couple of options. I ended up going with a Hard Disk Drive Shipping Box - Slotted Storage Container Package from Tek Source Solutions. This ended up costing around $35 on eBay and they claim it will hold 20-24 3.5" drives or I can double them up to store 40-48 2.5" drives.
I don't have that many, so I can use this to store the few drives I have and maybe fill up the rest of the box with other similar sized cards, RAM, etc.
Another item I found was the HDD Paper Storage Box with Cover (5-Bay) from Brando Workshop. This was a modest $16 to hold five 3.5" drives.
Both of these are primarily simple cardboard boxes, so I'll probably leave the hardware in its respective anti-static bags while in the box.
What I wanted to get was one of the foam containers from ProStorage such as their ProStorage18, but it's $80. It looks like the entire container is anti-static, so I imagine I wouldn't need the drives stored in their anti-static bags if I got this.