I don't like the "Kill X monsters" quests because those rely completely on the mercy of the Random Number Gods, unless there is an area which specifically has those. I particularly REALLY dislike ones where you need to get Rare Item Drops to proceed. if they're optional, that's fine, but if they're part of the main story, avoid those.
When you get down to it, just about EVERY quest in a computer based RPG game IS some type of well disguised fetch quest, a "Get to this location" quest, or a "Kill X To Proceed" quest.
That being said, a really GOOD mandatory quest is crucial to the story, advances the plot AND gives the party time to level up. In Chrono Trigger, for example, here are the first few story items, after going through the Time Portal in order:
1. When you reach the Castle, meet Marle ("Fetch" her)
2. Marle disappears, so you must do the "Find the Queen" fetch quest to save her ancestor
3. Defeat a Boss
4. Return to the present ("Get to the Time Portal")
5. Chrono escapes the prison after being unjustly scheduled for execution
6. Party lands in the Future
These are all examples of very GOOD quests. It's not because they're original, really. What makes them good is how smoothly they tell the story. The "Save the Princess/Queen" quest is as old as it gets, but it's just the beginning AND sets the stage for the Time Travel motif ("Events you do In The Past affect The Future") of the game. So it tells the story so well that you THINK you're doing a cliche "rescue the queen" quest --- and you are --- but the "save the future" is a great reason.
I remember I was shocked, the first time I played the game, when Chrono was scheduled for execution when he returned to the Present. So, already, the game sucked me into its world. And that was, maybe, 2 hours into the game.
If you do your game well, players will be sucked into your game world before playing it for very long.
The quests themselves are PLENTY of opportunity to level the party up, but it doesn't feel "too grindy" because your party always has something specific to do. And the plot itself has plenty of twists and turns.
That is what makes for good Quests. Fetch quests all boil down to "Get Me This MacGuffin" but creative writing can make them anything:
"Save the Princess"
"Reverse the Deadly Curse"
"Get the Idol" (Raiders of the Lost Ark fun)
"Find the password to the computer"
Also, minor NPCs besides offering hints, can really add a lot of flavor to the "fetch quests" and tell more story, such as in the "Deadly Curse" one, some might be victims of the Curse (Dragon Quest IX), for example.
But I'm not a big fan of the Kill X creatures quests. I don't see how those would tie into the story --- "Kill 8 Bugbears and I'll give you this Sword" I can see the Kill a Boss quests filling in nicely though ("A Bugbear murdered my wife. If you kill that particular one and bring me its head, I'll give you the sword we were going to give to our son.")