The USB Blaster is the way to go for simplicity, just add the 10 pin header for active serial configuration and the correctly sized EPCS device for your Cyclone III. Make sure you have the 10 pin header for JTAG as well, with these two headers you can validate the Cyclone III directly, then program the bitfile in the EPCS for power on configuration. Both of these headers are documented in the configuration schemes in the Device Handbook. Look for AS or Active Serial configuration.
If you have a Microcontroller or CPU that has flash and memory, you can have it configure the Cyclone III though several methods, I prefer pasive serial mode in this case.
Then it could be possible, if the CPU supported USB directly you program though that interface, but it's really a limitation of the CPU you use.
Many of the new development boards from Altera basically have a USB blaster built into the board. This is nice, since it doesn't require a separate USB blaster, but you need a MAX II device and the code from altera to support it. I haven't gone this route yet, so I don't know if the USB Blaster CPLD code is readily available or not.
Pete