Vehicles have always been a staple of the Halo series and although the Warthog always gets all of the glory, the Mongoose is the far more enjoyable method of getting yourself around. The Warthog is fun too but it's too big, gets stuck too easily, and it will inevitably lead to an argument ("You left me behind!" or "You drove like an [put expletive here]!" or "Oh yeah? Well you gunned like an [another expletive here]"). The Mongoose was great because it was speedy, small, and you weren't expected to bring anyone along for the ride (although you could and as gamers found out, putting someone with a rocket launcher in the backseat could be a lot of fun too). I think the lesson is that adding go-karts to any game situation automatically makes everything better.
Yoshi changed the way you played platforming games. Before it was just you, Super Mario. You walked or ran through the levels as quickly as you could, but you had no one else to help you with anything. Enter Yoshi: you now had something that could take you through the level and gave you a whole new method of dealing with enemies. And best of all he was selfless and loyal to a fault. Tough jump ahead? Might not make it? Leap off Yoshi at the last moment, and you were set. Yoshi fell to the bottom of a pit, but he didn't care there was always another egg close by. No wonder dinosaurs went extinct.
Hyrule had never seemed so enormous as when you first traipsed out into Hyrule Field in The Legend of Zelda: Ocarina of Time. Suddenly the world appeared vast and endless before your eyes, and you realized that walking everywhere was boring and slow as hell. Ocarina of Time is probably one of the greatest console adventure games of all-time, but imagine how tedious it would have been had you never gotten Epona. It was a gamechanger you could ride places much more quickly than you could before, you could shoot arrows while riding, and probably best of all you finally had a companion for your adventure that wasn't a super-annoying glowing fly.