Apparently, on the official Sega online store, they’re actually selling a mug with the famed “barrel of doom” pixel design on it.  
I want one, but it’s kinda expensive.

I accidentally figured out how to get past this thing while trying to spindash down on it, thinking I’d rip a hole right through it.

For some reason…I just knew what I had to do…maybe I’m just weird…

I actually figured this part pretty easily myself personally. Took me a week, or 2 to figure out how the hot air ballooons worked in that one lava level in Donkey Kong Country 2 though. (Didn’t know you could move them without falling off.)

Ah this part. It’s been referenced once before on derpibooru. Funny thing is I didn’t know about the arrows until someone told me when I was older.  
When I was a kid I tried the arrows and for some reason it didn’t work, maybe I only tapped it and didn’t hold it down long enough or something. When I was messing with stuff I never remembered the barrel moving from the arrow keys so I didn’t try it again.  
However, I did manage to get under. If you time it right, you can jump on it just right and get under when it’s going back down under. Safe to say everything past that point in the game felt rediculously easy….. And made gave me yet another reason to play knuckles on my long list of reasons to play Knuckles in Sonic 3 and Knuckles.

@Shadow Bolt  
Go back and finish it. Just hold up and down.

I SO HATED THAT PART! I’ve never gotten past that level.

Back in the day, you sometimes just had to figure shit out on the fly.  
Helpful directions wouldn’t just pop up and tell you what to do.
 
Alternatively, you bought NINTENDO POWER MAGAZINE (to help you find all the places to burn and bomb in Zelda)

All I had to do was go up and down?
 
UP AND DOWN?
 
WHAT THE (time over)

I freaking hated this.

Sonic: Oh shut up!  
Tails: Sonic you shouldnt say it!  
Sonic: Oh sorry about that princess!

What is both Sonic and Tails jump on the barrel, it might move then. LOL

It’s odd, I can’t remember ever having a problem with this part when I was a kid. As such, I was very confused when I learned years later that this barrel was actually kind of a roadblock to some players.