That aged classic, Commander Keen, is available in Flash form on Play.vg, along with a slew of other oldschoolers.
I played the hell outta Keen when I was wee, but my favorite was definitely Jill of the Jungle (unfortunately unavailable on the site). The combination of female protagonist and the ability to shapeshift in to different monsters was just irresistible to tiny, towheaded me. I was entranced with Rampage for the same reason, but Jill had a special appeal because you could morph into a bird and fly.
Tell me your favorite games of this era, and why you were so enamored of them.