I prefer the more post-punk/new wave sounding stuff, but I do enjoy "pure" gothic rock. As such, some of these are more post-punk or new-wavey than others. Others are certified "goth classics"
The Cure - Faith, Pornography, Disintegration
The Sisters of Mercy - First and Last and Always, Floodland, Some Girls Wander By Mistake
Joy Division - Unknown Pleasures, Closer
Siouxsie and the Banshees - Kaleidoscope, Juju, A Kiss in the Dreamhouse
Killing Joke - Night Time, Brighter than a Thousand Suns
Bauhaus - In The Flat Field
Some other bands you might want to look into...The Mission, Christian Death, Alien Sex Fiend, This Empty Flow, The Frozen Autumn, Pink Turns Blue, Katatonia ('98-'99 material mostly, the "depressive rock" period, though their 1994 rarity "Scarlet Heavens" is arguably classic gothic rock styled track), The Chameleons...
As you can see I'm mostly recommending you stuff that falls into the 80s umbrella of classic gothic rock, dark new-wave and pop, post-punk, and darkwave/deathrock stuff, which i'm sure springs to mind most often when the term "real goth music" is brought up.