I think Manyland is the most... sandbox-y thing I've seen, ever. It's a game about drawing pixel art and making it do stuff. You can customize pretty much everything, including the buttons on the GUI. You can draw your own custom buttons for the GUI if you want. You can create NPCs, AI routines for them (Or players, if you want to mind control people, apparently. I haven't tried that.) You can make lots of cool things, like a propeller hat that spins when you jump and lets you doublejump, or a randomly generated maze that regenerates itself at random (NPCs can place and remove blocks and pick random numbers), or a really cool animated dance floor, a clock that chimes every real-time hour and has working hands, the possibilities are crazily huge.
And the best thing is, it's free. You can visit manyland.com and it should just drop you straight in. Area transitions and respawns show you an ad, though. (It's web based, so you can block them.)
Transport between areas is simple: Type TO AREA_NAME_HERE in chat. That's it. Boom, you teleport. For example, you can type "to elsewhere" to go to the main area. (There's actually eight public areas that you'll be taken to when you request Elsewhere, but it defaults to Area 3. You can specify a particular area to go to instead of elsewhere by asking for Area # instead of Elsewhere.) Elsewhere areas are public, aside from a radius around the center, and they're infinite. And filled with spam most of the places you'll go.
There's some really neat stuff you can do, though. Go ahead and try it, you can log in with a Google or Facebook account FOR FREE to be able to build and draw new things. If you want, you can buy it on Steam for $9 and get a Steam-account-linked account (sadly can't be used on web, but they say that alts are totally allowed and encouraged.) with 200 free boosts. (Boosts do aesthetic things, like make you walk backwards, mostly. There are a few always-free ones like Teleport to Center, which is useful in Elsewhere, because try finding one point on an infinite plane of spam once you've wandered off.)
It should work on mobile devices as well on the web version.
This message was originally titled "Title" and contained one word. "Post." But then I decided to not get banned and wrote something in it.
Post.
The interesting thing is, areas have an URL that you can go to to warp directly to that area. For example, my roleplay world (very unfinished as of writing this) is manyland.com/aplacetoimagine (or say "to a place to imagine" in chat.)
