I think all three of these games are great in their own ways, which I shall explain. :3
I love Morrowind because, despite its age (and possibly because of it), it's a great in-depth RPG experience. Plenty of skills, a VERY broad armor system, a good list of racial selections, and a hearty list of spells and magical effects to use and combine. My favorite type of character was a stealthy thief that was good at restoration, illusion, and alchemy.
Oblivion was a fun game in that it gave some extra depth to the world, improving NPC behaviors and even adding interpersonal dialogue! That point there is one of my favorite details, letting you gain some extra information and even a quest from simply listening to the people talk amongst themselves. On the downside, the armor is more limited, the spell effects are less numerous (Levitation, you are sorely missed! T_T), and the enchanting and spellmaking system is much more limiting. I can only enchant items at the Arcane University? That's not fair! That and the faces. Oh Gods, the faces... XC
Skyrim is a beautifully made world with fantastic graphics and a great addition to the Elder Scrolls lore, though some points fall quite flat in my eyes. The magic system is even more stripped down than before, only letting the player use the basic spells that one finds in books. The enchantment system has been completely separated from the standard spells, and enchanting (AND Alchemy) can only be done at special worktables? That's kind of a dick move if you ask me. What if I'm cripplingly low on health in the middle of nowhere and have a load of ingredients that I can make health potions out of? Use the default healing spell? I'm not a mage! My Restoration is only 10!
As far as picking my one personal favorite out of the bunch, it'd have to be Morrowind. Yes, it's old and the graphics leave MUCH to be desired, there are numerous mods out there to remedy that very trivial problem.