In 'The Hobbit' (the book), little hairy people live in cozy houses and spend all day gossiping, eating, and being respectable. When a wizard arrives, a modern reader might expect fireballs to start flying all over the place, but instead Gandalf is really good at blowing smoke rings and telling stories.
When the group gets a magic sword later, the sword doesn't fly or talk or have a gun hidden inside it - it glows when certain monsters are nearby. This is unspeakably cooler than any vorpal +4 sword of lich-slaying with the ability to summon and command dragons.
Later in the story when Bilbo gets his ring, it is the most exciting, magical, even scary thing in the world. Rings of invisibility are always fun, and in an rpg, lead instantly to mischief, but this didn't feel like that at all. This ring felt special.
"Magic" doesn't usually feel special. Fantasy settings are so full of magic and whimsy that its not exactly news-worthy when something 'arcane' happens. It's the daily weather - clear, with a chance of lightning, but there is an orc front coming in that could put a damper on the festival if the heroes don't get back from that dragon riding competition in time. Also, a word from our sponsor: the innkeeper is now carrying a +5 vorpal sword of dragon-command, so those of you with the +4 model that is getting sort of old can finally get that upgrade we know you have been waiting for.
Tolkien's world is one of the most magical fantasy worlds out there, but its not because its overflowing with magic - there is actually very little outright magic in the world, and the strangeness is situated in space such that most characters would never encounter it. The world is magical because its sort of mundane. The humans don't live in a whimsical fairy land - they've never even met Dwarves or elves, and the things they worry about are political intrigue or land disputes. Battles are things of legend, not the thing you might attend this Saturday if nothing better comes up.
We instinctively worry that a mundane world is a boring one, but the world of Tolkien isn't boring at all. The black arrow that takes down Smaug is not some magical dragon slaying artifact, its closer to a lucky coin - and that makes it more magical than any lightning storm that an archmage could conjure up to strike the dragon from the sky.
Not mundane enough? What about when the pleasant but shy neighbour who sort of keeps to himself comes over for a little neighbourhood get together. They start talking about vegetable gardening, and he just keeps insisting there's no great skill to it, just time, and when pressed, he laughs and tells them about some of his tricks. He talks to you about how you can keep pests off your garden vegetables by making little homes for toads in your garden out of coffee cups, and you won't need pesticides, and he's showing this nerdy humble-old-man joy at being able to talk about his hobby while laughing at himself that is just charming. (story is from a CoC actual play podcast)
Imagine that some strange blue weeds start to take over his garden, killing one plant after the other, and this guy gets a little ill at the same time. That's something to investigate, that's weird. What is going on? Even a few weeds can become interesting and scary.
But if you imagine instead that the sky is raining swords, then a few weeds and a sick old guy doesn't really raise an eyebrow. Thank goodness he only has evil plants to deal with. We have The Solar Sword Slinger to contend with.
If you tone things down a bit then you can suddenly appreciate how nice it is that the kind homeless man who lives nearby has fallen in love, and how cute it is that he's trying to attend church now because his new friend is making him.
If you want to kill him or turn him into a monster later on, great - now somebody will actually care about what happens to him and those around him, because they had a chance to notice and feel something. The event becomes shocking and invested with this energy that is impossible if half the townsfolk were already werewolves or vampires in a big feud that constantly threatens the PCs lives.
For something in The Avengers to even register at this point, the entire universe needs to be on the brink of annihilation and a character might as well be invisible unless they are utterly bizarre or world-breakingly powerful - and even then, everything is like that, so they still fade into the background.
Magic can't exist without a backdrop of normalcy. The experience of magic, more than anything, is an experience of contrast. If everything is magical, nothing is.
That is, anyway, if you are going for that feeling of 'magical magic' - if you are going for a different experience, like action or surreal creativity, then magic gives you a lot of freedom to create what you like, which is great.
Note: Its possible I've forgotten some parts of The Hobbit since I read it last.