Unfortunately, I don't know what the problem is, so the following is a bit of a scatter-gun approach.
Self-powered hub.
It is possible (not likely, perhaps a tad more likely if your MBP is a 13″ one) that there's an issue with USB power. If you have one, try connecting a thumb drive through a self-powered hub, ie, one with a separate power supply (not a bus-powered hub).
New user.
Create a new admin user account. Restart and log in as the new user.
Try a thumb drive. If it shows up in Disk Utility, no need to perform the other steps.
Safe Mode.
Shut down, then start in Safe Mode, as described here
<http://support.apple.com/kb/HT1455>
Try a thumb drive again. Then restart as usual (the first start after Safe Mode takes longer; that is normal). Try the thumb drive once more.
Reset NVRAM.
It is possible (not likely) that a setting in NVRAM is causing an error. Follow the instructions here
<http://support.apple.com/kb/HT1379>
to reset NVRAM.
Reset the SMC.
Follow the instructions below
<http://support.apple.com/kb/HT3964>