FlapMMO, a massively multiplayer version of the sadly defunct Flappy Bird (not officially sanctioned), is that rare gem that delivers precisely that. In fact, it delivers everything you could ask for in the genre -- no combat, no levels, and a wide-open world to simply explore. It even offers exclusively horizontal progression (since that's the way the screen scrolls, you can't go backward).
If all this sounds too good to be true, you should consider also the fact that the game is entirely free-to-play without so much as a cash shop. Chat functions are currently limited, as is character customization, but there's no word from the developer on whether or not this is part of the design or something that will be addressed in the first expansion. You might want to consider giving this wide-open combat-free exploration simulator a try if you've got some free time on your hands.