When somebody even mentions "sidescrolling platformer" during a conversation, our minds immediately picture the original Donkey Kong, Super Mario Bros and Sonic the Hedgehog. These three games are the pillars and pioneers of the platformer genre with each game adding it's own spin to it. I still remember, in the old days of the NES, I spent hours and days trying to beat the last level of World 4 of Super Mario Bros and the level kept on repeating itself. I was very young so I was confused as to why this level never seemed to end. My elder brother taught me the puzzle that the level had to be traversed in a certain way in order to reach the final boss, King Koopa.
Sonic the Hedgehog added exploration and speed to the otherwise slowly paced platformers with the gimmick of the player being able to run so fast that Sonic can run around a loop like a rollercoaster. The game also offered the player the chance to gain a higher score by beating the level as early as possible and offering a grade for it. This scoring system wasn't implemented before since scores/grades weren't the real point of playing a platforming game. The game also had a crazy level design with the designers being able to get away with it since Sonic was able to access most places thanks to either Tails, springs or his high speed making every nook and cranny of the level accessible to him. Look at the crazy level below from Sonic Advance!
One of the most famous arcade games of the 80s and probably of all time is Donkey Kong. This game featured characters from two of Nintendo's most famous franchises of all time. The objective of the game was to jump over barrels and climb platforms vertically as we try to save Paulene from Donkey Kong who is the antagonist in the game. This game was a major hit among the youth and really brought the video game industry back on track after the crash of 1983.
According to me, in terms of difficulty and puzzle solving, two games which are side scrolling but involve puzzle solving are Mega Man and Super Metroid. Super Metroid featured probably the most atmospheric music and environment and very elaborate maze like levels which kept the user engaged as he/she tried to figure out where the upgraded weapons and items to be collected are and where the level boss is.
While Metroid used puzzle solving on an exploration level with the user eliminating each route which led to a dead-end, Mega Man used puzzle solving through the items available in the inventory which helped the player traverse through the 8 gruelling levels. The game also offered the player the freedom of choosing any order of playing the levels. The game had weapons like the Air Man's lift which enabled the player to reach high platforms which are inaccessible.
To summarize, for me, platforming action games are my favourite type of games. I am definitely missing out on many games like the Donkey Kong Country games which feature the best looking and interactive environments I have ever seen, Legend of Zelda 2 which added sidescrolling levels to the traditional overhead view of Zelda games, the NES Castlevania games which are the finest RPG/sidescrolling/action mix ever.