The fact that, from about 1500 to about 1920 AD, learned people could figure out, with a pretty amazing degree of accuracy, what the world looked like: the arrangement of the continents, etc. – without using air photos or satellite imagery – just slow, step-by-step mapping by boat and by horseback.
Hummingbirds blow my mind.
Listening to complex music amazes me. I can start trying to pick out various instruments, rhythms, riffs, and so forth, and just get lost in it.
Along the food theme: who the heck first looked at an artichoke and said “I could eat that?” Was it the same guy who first tried magic mushrooms? Maybe he tried the artichoke while the mushrooms were still wearing off.
Ditto snails, lobsters, kiwi fruit, tripe, and squid. And what about the guy who watched someone else eat a puffer fish and die, and then said, “you know, if I prepared that differently, maybe I could actually live through it”?
They were making beer long before they knew what yeast was. The Reinheitsgebot (Bavarian beer purity law) was passed in the 1500s, and it specified that the only ingredients allowed in beer were malted barley, hops, and water. No mention of yeast. I think it was Pasteur that figured out what yeast were and what they did.
My guess on how beer got started: Someone made some bread and left flour outside. Either they had water in the bucket, or it rained. Then it started to actively ferment. Hmm. Tastes pretty good. Whoa, dude! A buzz!
Two decades ago a gigabyte was a scarcely known concept not yet realized by the technology of the time (AFAIK). Once storage capacity of this magnitude became more possible or at least conceivable the physical space required for it would have been gargantuan. Today you can fit a gigabyte’s worth of a data in a space no bigger than your thumbnail. How they can cram 8 billion 1s and 0s into that tiny space amazes me. Add to this the fact that such storage space can be had for under $50 whereas a decade ago a hard drive of this size cost ten times as much.
Seeds.
Now matter how you put them in the ground, the roots go down and the rest goes up. How does it know?
Oh gosh yes! I love to watch my Tiel and Quaker be-bop around their cages and think “you were once a dinosaur. Cool!”
The human body, but most of all the uterus.
I am amazed that an organ that is typically the size of a large coin purse can expand to the size of a watermellon while maintaining the strength to exert a tremendous amount of pressure and expell a human through a larger than average keyhole.
Then it can shrink back down and do it all over again. And in some cases again and again and again.
Programming languages. I understand, and am not amazed by, the fact that Command X in a programming language results in Action Y. But how does the computer know the programming language in the first place? And how do you just up and create one. On that note, it amazes me that UNIX has been around for decades, and what once ran a crappy terminal now is the backbone of something so visually attractive as what’s on my Mac.
There are animals that can use freaking sonar. It’s just built-in.
And, again, birds. They can fly. Something that for thousands of years we didn’t even think was possible to achieve, they’ve been doing for millions of years. If they hadn’t evolved, it’s entirely possible we never would have been inspired to figure out how to fly ourselves. No Wright Brothers, no Apollo… all because one type of dinosaur was able to fly above the post-comet dust cloud.
Flight has evolved independently 3 times. Without birds would still have insects and bats for inspiration.
I suspect the way this most often went was, “I wonder if I could eat that? Hey, Thag! Eat this, or I bash your skull open with a rock!” If Thag doesn’t get sick and die, the tribe gets another food source.
Car and truck tires. When you think about the abuse they take it’s amazing to me that they take it, often for 60,000 miles or more.
The fact that our finger tips can detect such minute traces of moisture.
Or you could look at it the other way - anything that needs such fearful armour and weapons must be protecting something tasty!
If you broaden the definition of ‘flight’ just a little, then it’s happened a lot more times - flying squirrels, the similar (but unrelated) sugar gliders, flying snakes, flying frogs, flying fish. Not to mention flight in the plant kingdom (again, evolved many times - sycamores, dandelions.
OK, a lot of that is just falling with style, but that’s quite likely how the ancestors of modern ‘true’ flyers started off.
Anyway… a simple thing that amazes me is that I can split a piece of slate and be the first person ever to see the inside - or I can just pick up a pebble on the beach and I’m very probably the only person ever to have handled it.
I have always been amazed with clouds.
They are massive things made up of water droplets & vapor. You would think that with as much as water weighs that the clouds should just fall from the sky.
Dust devils.
Lightning. All that electrical potential building up more or less from the movement of dust and water vapor.
The entire empire of the digital, basically built on combinations of only two states.
Oh fine, be that way. 
But I’m guessing no one ever dreamed of being able to fly like a bat or a wasp. Birds are far more inspirational. 
Speak for yourself. I love bats.
ETA
Nitpick- I should have said “Flight has evolved independently at least three times.” I’m unsure if the various flying insects have a common ancestor or not.
I’ve had DNA explained to me a dozen times and I just can’t grasp how it’s possible. It’s just pure magic to me. I find it wonderful that the very thing that made me what I am is so astounding that I can’t understand it.
Light emitting diodes. I understand how they work but they’re just so durable and beautiful.
My Dad loooves flashlights, among other things engineers love to collect, and he bought a multipack with I think five different flashlights in it. There was a keychain light in there that used just one LED, and is the size and shape of a medium-sized cockroach. I placed a quarter on top of it, and at least 60% of it was under the quarter. This thing is as powerful as, if not more powerful than dozens of flashlights I’ve seen, and is small enough to swallow if I had to.
Those “mini” flashlights that people keep on their keychains? Piffle. The tiny thing is only good from about a foot away at most. I used mine to survey my friends backyard which is at least 60 feet in length. I was walking through a park heading to a 4th of July fireworks show through a fairly dark area. I turned on the light so that I and others could see the slope ahead of us. Several people turned around wondering where so much light came from.
So, yes, LEDs are fascinating and are starting to take over the market that small incandescent bulbs once had.