A very short starter list of Goth bands:
Bauhaus
This Mortal Coil
Dead Can Dance
Clan of Xymox
The Sisters of Mercy
Alien Sex Fiend
London After Midnight
The Southern Death Cult (before renaming to The Cult)
Bands listened to by a lot of Goth kids, that aren't necessarily Goth:
The Cramps
The Creatures
Siouxie and the Banshees
The Cure (particularly their early work)
The Smiths
Nick Cave and the Bad Seeds
Nine Inch Nails (particularly the early work)
HIM (for reasons I can't comprehend)
and yes, Marilyn Manson. Though, IMO, Manson is more shock-rock (a-la Ozzy Osbourne, Alice Cooper, or Screamin' Jay Hawkins) than Goth.