IMO They have brought back the following classes in a round about way:
Barbarian (which was an option along with Bard Class in the original Diablo in .cfg file)
Witchdoctor ( Combines Druid with Necro from D2)
Wizard (Sorceror/ess D1, D2)
Monk (Hellfire, I think combines Assassin with Paladin)
A ranged class would complete the line-up possibly with more supporting skills like the paladin if that hasn't been fleshed out with the Monk class. Or possibly Offensive curse like abilities if that hasnt been fleshed out with the Witchdocter class.
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Barbarian (which was an option along with Bard Class in the original Diablo in .cfg file)
Witchdoctor ( Combines Druid with Necro from D2)
Wizard (Sorceror/ess D1, D2)
Monk (Hellfire, I think combines Assassin with Paladin)
A ranged class would complete the line-up possibly with more supporting skills like the paladin if that hasn't been fleshed out with the Monk class. Or possibly Offensive curse like abilities if that hasnt been fleshed out with the Witchdocter class.