Or the Clash for that matter.

Definitely check out the Clash, all brilliant stuff, you can't go wrong.

As for Sum 41... I can't really say because I don't listen to their music. But if you like it then it doesn't really matter if they're pop-punk or punk or not.

Here's a quote from Wikipedia you might find useful:

"Most [Sum 41] fans and critics agree that Half Hour of Power and All Killer No Filler were purely pop punk, but Does This Look Infected? started moving toward heavier styles, such as alternative rock and alternative metal,[45] with Chuck being mostly alternative metal. "

In some senses, personally I've always liked to think of it as a genre as well.

I think there's little more to it than that. There are pop-punk bands out there who are not well known. It's not about the fact that the band is popular, it's about the fact that they do have a certain sound. It's a sound based on the mainstays of pop music: hooks, catchy choruses, tight instrumentation, etc.

I mean, listen to how poppy this Blink 182 songs is:

I would agree that pop is a musical genre, yes.

But pop means POPULAR. That is the root of the word.

Yes?

That is the only point I'm trying to get across.

I like the beatles, and honest to god, some of those boy bands, SOME songs, not all. lol they are my guilty pleasure, but recently I found some "punk" versions of those songs I liked so now I don't feel guilty about it :p:

Yes. But as a genre tag it means "in the style that is popular" not "this band is popular".

Wikipedia has a good description of pop music, "Pop music as a genre features a noticeable rhythmic element, melodies and hooks, a mainstream style and conventional structure."

I like that.

IMO the term has changed over the years. When I was a youngster (in the very dawn of time) the connotations of Pop were of the popular and mainstream but there was a perceptive change in the 70's and the Punk / New Wave paved the way somewhat. Certain "punk" bands, say XTC for example began to put out what where described as Pop songs, catchy hooks and melodies etc etc.
This change may have happened earlier but I have no earlier memory of it.

In the end I have no issue with genre classification as I think that that at least attempts to help the individual understand as to what they are listening to.