If you look at Daggefell you are exactly what you want to be, no prophecy. Nothing.
Yes. In Daggerfall, you get sent on a mission to help a ghost find peace and find+destroy a "personal" letter. That's it, no big important world-saving event, and no prophecy that you're the only one to fulfill it. Even as you go through the game, it's essentially just a political power struggle in an area that's constantly in a power struggle, so nothing special. Even later one, the discovery of the Numidium and subsequent vying for control of it is not a world-ending threat, and you're not destined to be part of it (in fact, the Totem specifically tells you you're not the one it's meant for). The only time you're hinted as being special is when you're in Aetherius talking to Sheogorath, the proud, up-standing truth-sayer he is.
This was also the case in Bloodmoon. Though there was a prophecy, it was solely about Hircine's Hunt. You were not part of that prophecy, and you were not destined to beat the hunt. The hunt also posed no greater threat to the world outside of Solstheim.
In Morrowind you are somebody that looks like you could fufill a prophecy, but not necessarily the one. Others have failed, more would not have tried at all. Your success is a testimony to your power and if you wouldn't have done it there would have been no problem because Azura would have picked another.
I would disagree with that. Azura tells you in the opening movie, before you even see any real game play, that you've been chosen to fulfill the prophecy. This is further backed up by how you're the only one since Lord Nerevar that could wield Moon-and-Star, and the only one that could be cured of Corprus (if you talk to Fyr afterward, he tells you the cure he gave you killed everyone else he tried it on). So even though your character may be someone's pawn and not believe themself to actually be the Nerevarine, they're still chosen to fulfill the prophecy and would not have been able to do it otherwise.
In Skyrim you are as close to being the only one without actually being it. Any dragonborn could finish the MQ, hell maybe even some people that are incredibly powerful but not Dragonborn. Still another candidate could have picked up, it was however unlikely.
The thing I like about Skyrim is that it can be played off that there's no actual world-ending threat, at least until you get moving along the MQ far enough. People are freaked out about seeing a dragon in the opening area and think it's a sign of the apocalypse, but that comes from Nordic legends and children's stories (note that Hadvar and Ralof are both Nords native to Skyrim, where they will have been exposed to this since they were kids). There were dragons in the service of the Empire at least until Battlespire, which was the late 3rd Era IIRC, and the book Twin Secrets tells of a dragon encounter some time in the 4th Era, so that on its own doesn't foretell anything. And the dragons don't even start attacking en-mass until
Spoiler you kill Mirmulnir, take his soul, and get summoned by the Greybeards.
Though it would've been nice if the rest of the main quest (and guild quests...) didn't revolve around you being The Chosen One, it at least let you permanently shrug off the MQ before finding that out and without being a nihilist dike. In Oblivion you're told before you can leave the tutorial dungeon, and in Morrowind you're told in a dream sequence before you start playing, thus always putting the fate of Tamriel on your conscience.