One of the very basic LED circuits is a blinky using astable multivibrator. This is the circuit that I've made - with hand drawn and etched PCB and with incandescent lamps - when I was in high school for a PCB making contest and won. I guess it still has sentimental value for me.
Now with LEDs instead of incandescent lamps, and USB power instead of batteries, here's the USB Blinkly.
I integrated the USB plug into the PCB, so it's simpler as well as economical. You can plug USB Blinky into any USB receptacles - computers, chargers, everywhere.
Step 1: Circuit
Current draw from the USB port is slightly under 5mA.