In most cases, you absolutely do need a form of I.D. with you before you fly; failing to provide a valid I.D. will prevent you from flying.
If flying locally then a photo I.D. should be sufficient, such as a driving license - though if traveling from abroad then you'll need to bring your passport along with you.
Not always needed but where a photo I.D. is needed is in major cities or helicopter ride companies who fly out many tourists.
Locations where I.D.'s are needed are in the USA, but so does it apply within Europe.