Mario has had a few different RPG series but the one I stuck to the most was definitely Mario & Luigi due to their challenging battle system.
It's like a normal RPG battle system except it incorporates more use of buttons and thus becomes partially dodging and then timing your attacks. It also makes it so you have to study your enemy to defeat them, all while having to be REALLY fast. It also incorporates platforming and puzzles when not battling.
I really love this series on how it still really FEELS like a Mario game even though it's in the RPG format. Also, the story is nice most of the time, although sometimes they fallback on the "Save Princess Peach" plotline a few times, but that's standard Mario.
I think my favorite in the series HAS to be Bowser's Inside Story, but what do you guys think?