Classes I think 5e DnD are missing:
- Warlord
- Summoner/Pet focused class ... note that I think this should be more along the lines of a Pokemon trainer class, so a PC that derives the majority of their power from their pet.
- Psionics
- Monster classes. Specifically the Lycanthrope and Vampire, but can pitch others
Classes that would be nice to have to increase the diversity of player options and mechanics. Most of these are supposed to be quite different from the Core classes and play mechanically differently. If they wield magic, they aren't spellcasters like Wizards or Warlocks.
- Incarnum
- Metamorph class, a pure shapeshifter
- A Martial Arts class, wielding something like Tome of Battle, but my preference would be a twist on the 13th Age Monk
- Other forms of Magic ... Shadow Magic, Binders, Truenamers, for example.