I don't know if it's accurate to say that an entire run blew my mind, or more like parts of it.
There were a few that blew my mind throughout most of it, but it's really unique segments that stand out as opposed to an entire run.
Morimoto's SMB3 blew my mind when I first saw it, being so insanely fast compared to normal play (a novelty which quickly wore off with other TASs), as well as some amazing moments such as the run hop high in 1-1, or the 99 live stomp, which the movies which obsoleted it all adhered too. Another big part was shooting at things before they appeared, although many movies made since do a much better job at it.
Morimoto's Gradius was crazy for the always take speed idea, and doing figure eights and other crazy things.
Bisqwit's Castlevania was extremely novel, and introduced so many standard TAS ideas, which blew my mind when I first saw it, just realizing that you have to think about optimizing to such a level. Ideas such as use knock back to your advantage, throwing away items you don't need, abusing enemy collision and other things, working closely with spawning rates. I was also amazed when I first saw it to see Simon jump over one of those wide knights, no real player would attempt it. The most recent run is amazing for the precision, the route planning, and all the other stuff. Each run was filled with shocking moments of: Hey I never would of thought of that, and more so, none of the previous TASers did either!
The first couple of SMB2's by Bisqwit weren't that great. But then SleepZ joined, and later Genisto, and suddenly the three of them were doing run after competing run finding new glitches and stuff I don't think anyone every would've dreamed of, plus each new novel idea they had to eke a bit more speed out of it. Each new glitch and idea was jaw dropping.
Bisqwit did runs of MM and MM2 which were better than Morimoto's, and really started doing all sorts of novel things with the magnet beam, insane precision, such as having exactly one unit left all over the place, and glitching out borders of the screen. Bisqwit's first bot run was downright amazing for seeing jaw dropping amazing random abuse for powerups, jumps which were way too precise and lucky to be real and so on. Later MM2, the first big group one surely shocked everyone with Woodman's level.
Once TASing was raised to the level it is now, I'm rarely shocked by a run as a whole, but surely there are moments. HappyLee's 6-2 for example. Arkanoid as a whole... Many moments in various iterations of Super Metroid. When the shell/enemy bounce back was discovered, and used in SMB2 full run, Super Demo World... The instana-kill in MM7.
For me, being a recommend worthy run, is when someone who really knows the game watches a run for the first time and frequently yells things like "No, he did NOT just do that!", "That's not even possible!!!", "Who the heck came up with that idea? It's insane", "Glmp... (water goes down lungs, and eyes bulge)".
Warning: Opinions expressed by Nach or others in this post do not necessarily reflect the views, opinions, or position of Nach himself on the matter(s) being discussed therein.