Wonder Boy (Arcade/SMS/various)
My all-time fav jump'n run/platformer ever. Fast, colorful, just what I like. Classic.
Wonder Boy in Monsterland (Arcade/SMS/various)
I was disappointed about the game at first because I wanted another fast-paced platformer like the first part but Monsterland grew on me over the years and now it's up there with the original game in my personal hall of fame. Some tricky jumping parts and a RPG-style shop system, loads of levels and bosses, lot of things to do and many secrets to find.
Wonder Boy III - Monster Lair (Arcade/Genesis)
Monster Lair was a breath of fresh air for me. It went back to the original fast-paced platformer formula and is even less forgiving than the first part, you gotta catch all the fruits you can in order to keep your energy bar in the green. The game is split between platforming and horizontal shooting parts which might put some purists off but I like it a lot.
Quackshot starring Donald Duck (Genesis)
A somewhat underrated Disney platformer, nice level design, many different locations, great gameplay, not too challenging. People rarely talk about the game which I find kinda strange, it's no Castle of Illusion but great in its own right and good fun for a few hours.
Trolls (Amiga)
A rather simple but very playable and fun platformer. Collect all troll babies in a level to advance to the next, some tricky spots, nice graphics, good music.
Wiz 'n' Liz - The Frantic Wabbit Wescue (Genesis)
Not sure if this qualifies as a platformer, love the game a lot. You play as sorcerer apprentices Wiz or Liz and have to save all Wabbits in a level by collecting them as well as letters to form a different word for each level against a time limit. Collecting magic spell items and bonusses lets you create magic spells which may or may not help you with your task. "Frantic" describes the game best, it's really fast and working against the time limits gets your adrenaline flowing. Boss fights can be very intense. I find the game highly addictive but it definitely isn't everyone's pint of beer so give it a try.
Popful Mail: Magical Fantasy Adventure (Sega CD)
A great-looking and playing platformer with a good chunk of RPG elements, including a quite large inventory and NPCs. You start with one character called Mail but you can unlock two more and then switch between them at any time. Each character has different abilities as well as offensive and defensive skills and items. Excellent graphics and music, spot-on gameplay.