Tanking: ArchPaladin can get the job done quite well, additionally provides decent support in a group, and can function as an above average farming class in certain conditions. Also from what I know, I guess VHL is as good as ArchPaladin, if not better. Also, even though it's rare, if you've got UOK, that's also great at surviving with Resplendent Aura kept up at all times.
DPS: LightCaster and Legion DoomKnight(both new and classic) are undoubtedly top 2, bettered only by VHL and Chrono Classes imo, but if you're looking for more options, classes like Glacial Berserker, Chaos Slayer, Soul Cleaver, StoneCrusher could be worth looking into, even DragonSlayer General if you're gonna be fighting Dragon Types. Chrono Assassin is another class I quite enjoy using, although that does require membership to obtain.
DoT: StoneCrusher builds up quite a strong DoT over time with the last skill. Paired with an Arachnomancer it can rack up quite high numbers. Apart from that, LightCaster also has a decent DoT with it's last skill. Oh and Blaze Binder is basically all DoT, so that with Arachnomancer would give you quite nice numbers too. Also, if I'm not wrong, Infinity Knight is still available in game, so that's definitely an option if you feel like spending some money, although SSoT and Immortal Chronomancer would be much better options if that's the case.
Healing Support: LightCaster, Oracle, ArchPaladin and StoneCrusher basically. LightCaster and StoneCrusher also contribute more to the DPS of the group than the other 2, so they're a tier above imo, with StoneCrusher more or less being the best all round support class there is. ArchPaladin is not a bad shout too, as it constantly keeps debuffing the enemy alongside, and has the highest heals of them all.
AoE: BlazeBinder, Shaman and Vampire Lord are the best in the business for this. Haven't tried out the new BattleMage yet, but I've been told that it's become pretty good too. Alternatively if you're looking to fight >3 monsters at a time, Eternal Inversionist and Chaos Slayer can perform quite well too.
Lastly, not sure what you mean by generalist class, but if you want a jack of all trades kinda class, then I'll always recommend Chaos Slayer for that, since the switch up from farming to soloing is so easy and useful to do, plus it's a fun class to use. If not that, Darkblood Stormking does quite well in that category too.
That being said, with classes like LDK, LC and VHL in the game now, I think they can possibly be more efficient in farming than some AoE classes too, especially in favourable conditions, so if you've got any of those 3, you're more or less set.