How are you defining "dungeon crawler"? There is a pretty wide variety of sidescrollers you can look at, from the MMO MapleStory to old arcade-like games such as Zelda II, Golden Axe, a variety of TMNT games, Super Metroid, or newer things like Viewtiful Joe and Castle Crashers. Do any of those come close to being a dungeon crawler?

MapleStory allows the player to freely wander through the game world like that. With most RPGs the player is only going to want to be where monsters are the appropriate level, which is probably 3 or fewer places in the world; so it's questionable to me how much freedom of exploration matters. In MapleStory in particular, exploration isn't really emphasized because of the MMO nature of the game, which means it's unlikely to find anywhere in the game that there are no other players. But there are certainly sidescrollers that do emphasize exploration, especially the ones which are adventure games rather than platformers.

Things you should consider while designing one, well, it's the same as designing any kind of game: you have to identify what you want to make in terms of gameplay genre, theme of the world, amount of story, target audience, platform/controls, MMO or single player, and all that. Make a list of desired features, looking at these example single player games for suggestions.

To develop exploration, you have to give the player reasons to explore. Reasons to explore might be clues to a mystery about how the world works or what happened in the world's past to make it the way it is, or abilities the player could learn. Other motivations for exploration could include crafting ingredients or quest items the player needs to gather, or pages of story the player is trying to collect, or a special type of currency the player needs to expand, upgrade, learn, or craft something. In a multiplayer game it is possible to spawn a unique set of exploration rewards for each player, which are not visible to or collectible by other players. Or, collectibles can be in a standard spot but become no longer visible to players who have already collected them.

River City Ransom is an old gem that I enjoy that has an open-world setting that lets the player explore the city in a side-scrolling kinda way. Its worth checking out to give you an idea of how it can be done.

That and it's pretty dang fun IMO