1) What type of character concepts do you expect to see in a Fantasy RPG?
Since this thread is explicitly about classes, I will use the following answer, but I would probably give a different answer if we were talking about a classless RPG.
There are actually a fairly large number of classes I would expect to see in any RPG. A conservative list would be...
The armored knight who can protect his allies.
The offensive magic-user who can rain down magical destruction on his foes.
The magic-user who is skilled at healing and has mastery over holy power.
The agile thief/skirmisher.
A dedicated archer and/or gun-user (depending on setting and tone of the game).
The classic monk/barehanded-fighter.
A lightly-armored warrior who combines swordplay and magic.
A mage who summons and controls powerful magic creatures.
Alternate melee combat concepts that use different styles or weapons.
Ninja.
A mounted combat fighter, preferably one that uses exotic and cool mounts, such as dragons or griffins.
Classes built around song and/or dance, that have powerful support or offensive effects.
The berserker/barbarian/wild-man class.
2) Of these concepts, can you think of any mechanical executions of that concept that you particularly like?
There are all kinds of versions of these that I like. For example, I am very fond of the Bard and Dancer classes from the videogame Final Fantasy Tactics, and the Bard from Final Fantasy III. While it is a bit complicated, I like the "class" used by the character Gau in Final Fantasy VI as a version of the Berserker archetype. The Sorcerer/Swordmage from Final Fantasy V is elegant and solid. The armored and mobile Dragon Knights of Fire Emblem Radiant Dawn are both a lot of fun and a testament to how you can create great classes without special mechanics whatsoever.
3) Do you have any original concepts for a class, or a new spin on an old concept?
Plenty. I'll save them, though.
Of course, any given class system is always going to be incomplete in comparison to the vast array of different character ideas seen throughout the fantasy genre that can be easily converted into distinct classes. As such, there are always more class ideas, and they tend to be more fun and interesting the further you get away from the default list.