So far I've given you some prog, classical, Big Band, and a bit of hard rock. Time to flip the channel to one of my guilty pleasures...
There is a style of heavy metal music often referred to as Swedish melodic death metal, aka Gothenburg metal (named after the Swedish city where it was born). One of the founding bands is Dark Tranquillity, arguably the least changed from their origins than the other groups. They blend heavy playing and coarse vocals with a more neo-classical sensibility that still makes room for melody. If classical music had continued and taken a darker evolution, it might have sounded like these guys.
"Cathode Ray Sunshine", from their 2002 album Damage Done, was the first Dark Tranquillity song I ever heard.