Use of ULN2003 for LED current drive
Take a look at this firstly: -



It shows the common pin connected to all the individual outputs via individual diodes. Now see this diagram - they have used common but also they've used external 1N4004 diodes: -



Don't ask why they did it this way - it seems to me that the internal diode should be as good as the 1N4004. Anyway the diodes catch the "back emf" from the inductance of the motor or relay or solenoid or electromagnet when the transistor is turned off.

If you are just driving LEDs or non-inductive loads you can use it with common tied to the highest voltage or leave it open.