I hate to dig up such an old question, but these answers need help. There are a number of different 2U cases that feature 12x3.5" hot swap bays (3 vertically x 4 horizontally -- See Supermicro's SC827), , and even some that also have an internal bay or two (http://www.servaris.com/servers_m2100.php). It's dense, but not impossible. If you want to get a little crazy, Supermicro's SC847 supports 45 hot swap drive bays in 4U (no motherboard) or 36 with E-ATX motherboard, and someone makes a case (the RMC5D2) with 48 vertical hot swap bays with room for E-ATX board and I think 7 full-sized cards in 5U.
I believe this is for Facebook's Haystack system for photos, where they use a RAID 6 controller to connect the drives. You can buy a low profile one that still supports 12 drives or use a riser card.
Facebook uses a Hadoop system to analyze everything that happens on the site (multiple TB/day). It skips RAID disk arrays and makes the entire machine redundant by splitting large files into 64MB chunks and writing each chunk to multiple machines. For this you can get a motherboard with 8 ports and cheaply add 4 non-RAID ports. I'm pretty sure these machines don't have so many drives, but the technology is based on stuff that Google is doing. Google does have racks of 12 drive RAID free machines, and a lot of interesting computer designs. They're almost big enough for custom parts to be a volume order of commodity hardware.