In 2006 Nintendo tried to bring back old school Mario platforming and New Super Mario Bros smashed on the scene to great reviews. I'd say it's a nearly perfect Mario game in that it's fun and feels challenging enough. The first handful of Worlds aren't terribly difficult but they are inventive and fun. The last few Worlds, 8 in particular, ramp the difficulty up considerably which makes beating them all the more rewarding.
Nintendo brought Mario to iPhones and Androids recently and I much prefer a traditional play style Mario game like New Super Mario Bros to the tap to play Mario Run. Mario Run is just about the best you can do on a phone but New Super Mario Bros is some of the best Mario platforming around and the traditional style d-pad thumb controls on the 3DS really make it shine.
If you have a DS or 3DS I recommend adding New Super Mario Bros to your collection. The "New" Mario platforming series has received a couple sequels such as New Super Mario Bros Wii, New Super Mario Bros 2(on 3DS) & New Super Mario Bros U. All of those games look great and I plan on picking them up at some point. It seems Nintendo is hip to keep the "New" Mario platforming franchise going and I expect that they will bring a new game to the Switch at some point to keep the old school platforming alive for their new shiny system. And if they do and you have a Switch I recommend you look into it because if it's anything like New Super Mario Bros it will be well worth playing.