I know different games use different techniques and units of measurement. In Starcraft II one range for attack is about the width of one zergling. In Guild Wars the range is some fraction of the compass or aggro range (Spears have ~0.7x aggro range, longbows ~1.2x)
Most (or all?) meelee champions in LoL have an attack range of 125. The attack radius for range champions differs quite a bit, e.g. 425 for Urgot, 510 for Twisted Fate and 550 for Heimerdinger.
I wonder how is range exactly measured in League of Legends?