I'll admit I don't exactly have the broadest taste/knowledge of metal but i'll give it a go
Judas Priest - Painkiller
The first song I thought of, typical I know but this song blows away everyone who listens to it, absolute powerhouse of a song.
Black Sabbath - Symptom Of The Universe
Incredibly influential and lead-heavy song by the godfathers of metal.
Motörhead - Overkill
Fast as hell and very influential to the thrash metal movement.
Iron Maiden - The Rime Of The Ancient Mariner
Not the typical Maiden song choice (was either this or Hallowed) but I pick this one as I see it as the quintessential Maiden song.
Megadeth - Holy Wars... The Punisment Due
Incredible Thrash song with unbelievable power.
Deep Purple - Highway Star
Always been a bit of conflict on whether these guys are Metal/Hard Rock but I see this as a classic metal track.
Metallica - Master Of Puppets
As rickety as these guys discography has been you can't deny their impact on the metal scene, and this is their best song imo.
Slayer - Angel of Death
Brutal and blisteringly quick thrash song from Slayer.
Dio - Holy Diver
Brilliant track from the little man with the huge voice.
Accept - Fast As A Shark
Another heavily influential track for speed metal and metal in general.