You can connect SOME usb flash drives. I had about a 50/50 success rate. If yours is a sandisk or kingston, which both come with bundled software on them, that often triggers the 'too much power' warning. (Big flashy LED's also try to pull more power than the iPad has been programmed to put out)
However, like Dianovex says, even if you get one connected all you can transfer are photos or videos and even those have to follow a very specific naming convention.
One thing that often confuses people is that prior to 2011, iPads used to allow more USB things to be plugged in. Keyboards, headphones, microphones, etc. but a software update in 2011 apparently tweaked the power allotted to the 30 pin input which rendered most of those things unworkable.