This list is not the only bands. If other bands get brought up, I will have no problem discussing them.
There is a non-pop punk section/blog post I plan on going more into.
But, to stick to pop punk first.
Some examples:
The Wonder Years (Yes, it's a band. Not the TV Show)
The Story So Far
Man Overboard
Citizen
Title Fight
Neck Deep
Handguns
Set Your Goals
Have Heart
State Champs
Such Gold
Tigers Jaw
Major League
Real Friends
The Swellers
Transit
Four Year Strong
Touche Amore
With The Punches
(mentioned below are some bands that people typically like when they like pop punk, not all bands are "pop punk")
Brand New
The Front Bottoms
La Dispute
Balance & Composure