Bugs Bunny is the foundation for our ideas about Saturday-morning cartoons--he's laid-back and doesn't appear to have a care in the world, but when he's in danger he defeats his enemies immediately and in the most humorous way possible. The ease with which he does things is inspiring, even if it's completely impossible. Bugs imparts the lesson that we can shape reality however we want if we need to solve problems. He does things his own way and without relying on anyone, which also makes him memorable.
Darth Vader is quite the opposite of Bugs Bunny in most ways, being a moody Sith lord who rules the galaxy with an iron fist. It first appears that Vader represents the ultimate evil force who is bent on domination, but as the Star Wars movies progress it becomes clear that he's a conflicted character who is only in his current role as the result of a long personal struggle with himself and manipulation by an evil emperor. This is why people remember Darth Vader--he is complex and human underneath his unforgiving dark mask. That, and he's pretty cool as an evil lord.
Mario's brother Luigi (from the games, yeah) is in my opinion one of the most memorable characters in the video gaming world. At first glance he's just the sidekick of Mario, the tag-along, tall awkward guy who nobody knows. But underneath Mario's fame Luigi has developed a closet personality and lots of fans. He does everything in unorthodox ways (play as him in Super Smash Bros. to see what I mean), probably in order to differentiate himself from his brother. While Mario's adventures are all standard, rescue-the-princess fare, Luigi gets himself into much more interesting quests (like winning haunted mansions in contests). Luigi, I think, is representative of the importance of being different.