I've added a few that aren't on your list, but matter to me. Feel free to ignore them if you want a list without; I'll mark with asterisks.
Paladin
Summoner*
Sorcerer
Warlord
Avenger*
Swordmage
Shaman*
Ninja (if distinct from Rogue)*
Warlock
Monk
Druid
Bard
Rogue
Fighter
Cleric
Psion (and psionics in general)
Wizard
Artificer
Warlord / Swordmage —> I’ve not heard of these as official classes!
They were official in 4e, and had official equivalents (Marshal and Duskblade) in 3e. Both have pretty meaningful devoted fanbases that would like to see them given proper treatment as actual classes.
More or less, think of their position like this: Imagine if there was no Wizard class, but there were still Arcane Tricksters and Eldritch Knights, and someone tells you you should be happy to have not one but
two Int-based spellcasting options. You would, I'd argue rightly, demand that a class that
focuses on that Int-based spellcasting be included, that there's just not enough design space in the confined limits of a Fighter or Rogue subclass to truly articulate that theme.
That's how such folks feel about Swordmage and Warlord. The "Warlord Fighter" is to a
real Warlord class what the "Wizard Fighter" (Eldritch Knight) is to the real Wizard class. Likewise, a Swordmage class is not "Eldritch Knight, redesigned." It's a class that marries warrior-stuff and spellcaster-stuff from the ground up, united, inseparable, indivisible. To do weapon drills IS to do spellcraft; to practice your spellwork IS to practice your bladework. You could no more separate a Swordmage's "spellcasting" from her "martial prowess" than you could separate a poet's "vocabulary" from his "grammar"--to use one skill in any functional way
is to use the other skill, and vice-versa.