There are plenty of thin external hard drives available on the market these days. The Seagate Seven 500GB Portable External Hard Drive (STDZ5004000) happens to be the one of the thinnest hard drives money can buy (the thinnest 500 GB portable HDD according to the manufacturer). It has a strong stainless steel enclosure and is 7mm thin. In other words, it is thinner than an iPhone 6 Plus (which happens to be 7.1mm thick).
Seagate Seven has a 5mm HDD inside. It does not require an external power source. It measures 122.5mm (H) x 82mm (W) x 7.00mm (L). Thanks to its USB 3.0 support, you can transfer files quickly. Sets you back under $100 at this time.