All the "normal" games (Donkey Kong, Mario Bros., all the SMBs, the SMLs, World, Yoshi's Island, Galaxies, etc), I count as absolute canon. Also canon is the fact that Mario enjoys racing, playing golf, tennis, and other various sports as well as board games, although not necessarily everything that is said or done in the games about those things.
I see Paper Mario and Mario & Luigi as existing in their own alternate realities, like the Marvel multiverse. A lot is the same. Bowser kidnaps Peach all the time, the Mario Bros. are renowned heroes, Yoshis live on islands, doodle dee doo dah. But they've got such unique feels to them and each seems to have rules that the others break. Luigi is a chatterbox in PM, doesn't say a word in M&L; meanwhile, both are free to talk in the main series. In both RPG series Mario's hammer is nearly as iconic as his jump, but he rarely uses 'em in the main series. Yoshis clearly speak whatever language everybody else is using in Paper Mario, but are restricted to "Yoshi" everywhere else. The rules of the fiction just don't agree.
And Super Mario RPG is in the same canon as Final Fantasy.
