Well, honestly, it's actually fun and interesting to try and string everything together, canon or no canon, Mario or not Mario.
Just because Nintendo didn't say Mario has any official canon and his games focus on light-hearted fun doesn't mean people are prohibited from coming up with their own ideas.
I wholey advocate filling in the blanks ourselves. It's just that when people do talk about it, they constantly refer to "canon" and "not canon" as if there's as an actual, official canon to base things on, which there clearly isn't, and that annoys me.
If Mario characters had some recollection of the past themselves, then that'd be cool. See, it could work well to be implemented into a game because it wouldn't hinder anything that makes the games great. If people caught the reference, then it'd be awesome for them. If they didn't, well, simply skip to the next text box without knowing and move on. That's all I'm really asking for, canon-wise.
Bowser and his minions always acknowledge past. He acts like kidnapping Peach is a daily chore at this point.
Luigi acknowledged Mario Kart, Mario Golf, Mario Tennis and Mario Party in Paper Mario.
Presumably Mario himself recalls past events, but we never get to hear him speak his thoughts on the matter.
Keep in mind, most of this occurs in the RPGs, where there's the most dialog and of course the most story with which to fill it with. The platformers delve into this less because....well, they're platformers, and they have less cutscenes, and the characters say less.
Not to mention, if done poorly, recollecting past events tends to come off like Family Guy cutaways minus the jokes. If they draw out recollections too much it just slows everything down. This is why I prefer past references to stay as simple little background bits that are only there for the player's enjoyment. We don't want this series turning into Sonic now, do we?
When no one in the games has any memory of anything that's happened in the past, Mario seems to become less of a "person" and more of "the guy that exists solely for the purpose of navigating levels" and it makes minor characters seem even more placeholder-ish (read: pointless). (Also, don't pick that last sentence to pieces. I know Mario is fictitious.) I know that Mario doesn't say a word or really have a personality or whatever because the idea is that you're suppose to feel like Mario when you play the games. Sorry, but when I get immersed into a game, I don't feel like I'm the character I'm playing as. Being immersed makes me feel like I'm watching a movie of sorts with the ability to alter the way their quest is progressing while I'm enjoying the ride. I don't feel like I'm Mario; I feel like I'm Mario's friend, in a way.
I don't think Mario was ever intended to be seen as a person within the context of the game. I've always felt that the character and I are one and the same no matter what game I play, especially if it's a silent protagonist, which Mario always is. Maybe it's a different strokes sort of situation.