Super Mario Land is, at least 1. Cant remember how 2 played (6 Golden Coins), but I know for sure after that, with Wario Land, it developed into its own series.

SMW2 Yoshi's Island is also what I consider a spin-off, which then developed into its own series.

Edit: Maybe I should actually answer the question, heh... I think all the NSMB games is also part of the series, but the 3D games aren't entirely related.. Well with 3D Land and World I guess they tied those ends together. 

Also, I consider NSLU part of the series, just as much as The Lost Levels is. 

Edit 2: Remember that Mario Wiki is just another fan wiki. Not hating or anything, there's a good effort in there, but fan theories shouldn't have a place in a wiki with respect for itself, maybe just a little trivia section if it's important... The last time I visited mariowiki, every article was filled with fan sections etc. 

if Princess Peach is kidnapped or playable then its a main Mario title.

All four do count...although only two of them are good

Super Princess Peach feels more like a Yoshi's Island game though. Great game nonetheless

I think it is more a two timelines thing. In SM 64 the timelines branched. One became a complicated 3D Jump n Run, the other got stuck in one of the 2D picture frames and evolved in the "New" 2D series, which is more canon than the 3D games imo.

Yeah the two timelines is how I see it. They are both part of the 'main' Super Mario series, but I look upon them as 2 distinct branches, The 2D series branch and the 3D series branch. Not really concerned about canon in the Mario series though.

Why not?

New super mario bros. are part of the super mario bros. series for the NES. 

But then again, where is the third timeline where Mario never beat bowser and hence bowser ruled Mushroom Kingdom and Peach was with him all the time? Is that Mario Kart?

Pretty sure that's Mario Party. Mario and friends live in servitude to the enjoyment of lord Bowser. This is why Mario PArty has the Bowser Party mode