Monk is on my short list, though not quite how you imagine. It would be an undertaking to give him unarmed attacks as a weapon, so he's melee based - only gets bonuses if he isn't wearing armor, but they're pretty big.
Monk sounds like it'll be interesting. Might use that in a try of an armorless playthrough.Current stats are melee damage, crit, defense, life regen, and endurance. Bonuses are big, because you're losing out on anything you'd get from armor, including set bonuses. Armor only counts actual pieces of armor, so you can wear whatever accessories.
Couple more thoughts on new classes, I guess. If they're similar to classes already in, that's cause I'm not checking the classes already in.
Fast melee guy. Gains melee speed and movement speed, decreases to all damage except melee.
Maybe an active of 3-10 attacks with the item currently in hand at once, getting more in amount the further in the game you are. Basically - you swing a wood sword at the beginning of the game 3 times right away, with all three actually hitting. Later on, you use 10 daybreaks right away, hitting the target with all of them. May need a rather high cooldown on that one. Maybe not the increasing amount over time, or not that much.
Sky mage guy. Gains much higher magic damage, mana regen, and mana the higher up you are, less the lower you are. If at top of world, you'd have immense power. If at bottom, you'd be incredibly weak. Decreases to all other damage types.
Since Wall of Flesh may be a problem, unless you use other weapons than magic, perhaps the active could make the whole world affected by the gravity of space for 30 seconds, effectively making the world the sky. Needs a decently heavy cooldown, probably 5-10 minutes.