Speaking about catchiness...what are the best Pop-Punk songs?
I'm sorry but I love to listen to some of the genre's biggest hits sometimes:

1. Head On Collision - New Found Glory
2. Bleed American - Jimmy Eat World

...then?

That's not punk. I wouldn't even consider it pop punk.

https://www.youtube.com/watch?v=8-r-V0uK4u0 - Smashing Pumpkins - Bullet with Butterfly wings

Does this count?

If I get to decide, then no. Some people would sneak them into the grunge label, but that's mostly for bands from Washington (mostly Seattle).

Bomb The Music Industry! was pretty good at writing catchy songs.

Heroes Come Home in Boxes - The Fartz
Misanthrope - The Nihilistics
Blue-Green God - The Meat Puppets
Out of Step - Minor Threat
The Rub - Killdozer
Big Takeover - Bad Brains
The Shah Sleeps in Lee Harvey's Grave - Butthole Surfers
Do As You're Told - No Trend
Politicians - Raw Power
Ain't No Feeble Bastard - Discharge
No Government - Anti-Pasti

Circle Jerks- Wild In The Streets

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It all depends for me what Sub-Genre of punk. Like Pop Punk I would think Weezers "Island in the Sun" is a super catchy song.

Punk:



Hardcore punk:



Pop punk:



Island in the Sun:



Just sayin'