Well, I personally love exploring. Fetch quests? What does that really mean anyway? Yes, going and getting something someone wants and they pay you for it, is pretty much what 'adventuring' is all about in just about every game ever made.
I haven't run into any 'fetch' quests yet that felt like they weren't appropriate to the story being told.
A "fetch quest" is a term that refers to a quest that either has little-to-no significance to the main plot or doesn't hold up on it's own as a compelling story, that requires you to go and get something for an NPC. This "something" is typically mundane and boring and this NPC is typically a nobody. A fetch quest could have you go get something exciting and could be given by an important NPC, but if the game does nothing with the item, the NPC, or your actions after you have completed the quest, then it's still a fetch quest.
For instance, it doesn't matter if the king sends you on a quest to retrieve the royal family's lost legendary sword from a thief, if, upon your return, the king says "oh great thanks here's some gold" and that's the end. It was as much of a fetch quest as the no-name healer NPC who asked you to go get three common herbs to heal the sick because it didn't affect the main plot and wasn't a very compelling story on its own.
Some people try to abstract any quest that requires you to go and get something as a "fetch quest," but the term really only applies to low-significance quests as described above. If we take the same quest outline (king sends player to get sword), we can easily turn the quest into a non-fetch quest.
So the king sends you to find the royal family's lost legendary sword from a thief, as was the case last time. Only this time, instead of simply finding an enemy NPC with the name "Thief," killing them, looting the [Royal Family Sword], and returning it to the king, instead you find a named NPC that you can interact with.
Upon speaking with her, you learn that she is a descendant from the family that the current royal family kicked out of power centuries ago, and the sword is actually her family's sword, which is why she took it back. The game gives you three choices: kill her and take the sword, offer to buy the sword from her (her family has fallen on hard times, surely gold is more valuable than sentiment), or let her go.
But wait! It turns out that the king also sent a few of his own men to follow you in secret. If you choose to let her go, then they try to arrest both of you. The game gives you the choice to persuade/intimidate/bribe the guards, but failing that, it comes down to combat. After the player (and the thief, who obviously becomes a friendly NPC for the fight) defeats the guards, he or she is given the chance to persuade the bandit to come work for the [Special Group You're Always Forced To Join In Every BioWare Game], and if successful, earns whatever perks that gives.
At this point, the player can return to the king to turn in the quest. If the player acquired the sword either by killing the thief or by purchasing it, then he or she can give it to the king, or choose to lie and say that the thief had allies and that all of the king's men were dead and the thief got away, and keep the sword for themselves. If the player sided with the thief, then he or she can also choose to lie, or perhaps even tell the king the truth (I guess it would depend on your character's station in the game, whether or not you could just defy a king).
By that same note, even if the quest does remain small, with the NPC named "Thief" and the limited options/outcomes, perhaps by doing this quest, later on in the game the king shows up in the main story and offers you support in some way. This, too, would make the quest more than just a mere "fetch quest."
Origins was full of these types of side quests. Inquisition doesn't seem to have any.