You've probably seen master maps in most of the enjoyable 2D games you've played.
These maps create a sense of place and can also make the 2D experience more freeform for the player. They are relatively easy to implement, but especially so in Game Editor.
Examples of this technique are seen in "Commander Keen : Goodbye Galaxy," "Xargon," "Platypus," "Fallout," any 2D game where you could choose your next area to explore from a larger overview.
In some cases, you can have areas that are closed to the player until they obtain a certain item, solve a given puzzle or have explored an existing area. At the start of your game, you'll always want to have at least three different choices available to the player so they can freely begin somewhere not too challenging or as part of an in-game tutorial on how to play using the most basic elements of the game, like running-shooting-jumping exploring.
One interesting twist is fog-of-war or discovery areas, which were not initially visible but become so later due to the solution of another problem.
My ambition in this regard is the hybrid. I am interested in games that allow me to explore a master map and then engage in either a traditional shoot-em-up or a platform game or perhaps even a fighting style game, all merged into a single experience and united by manipulations of the master map. One of my favorite arcade hybrids was LEGENDARY WINGS, where you have a 2D vertical shooter followed by an albeit simple platform level and a boss encounter. Too cool.
The project I am working on currently in Game Editor uses all these 2D design principles and I hope to post some screenshots of my progress soon, including my master map and accompanying information screens.