Can this be done? Is there a way to make it so that instead of square tiles on your maps, you can have hexagons that are connected to 6 other tiles?

It SHOULD be possible. It would be a heck of a lot of work, however.
In response to Jon88
So I guessed. Is there any way to actually code it in dreammaker?

In response to Dagolar
Yes, I think. Since regular PC games(including the ANCIENT arcade games) can do it, there's not much reason why you can't do it in dreammaker. It would involve creating everything from the ground up with objs and your own method of determining where exactly everything is and ehat it connects to. It would probably end up being too slow for a multiplayer game.
In response to Jon88
It can and has been done, however it is a serious pain in the patooty.

In response to sapphiremagus
dig through the forums on hex maps, and you should find a lot of posts that have talked about... it is a little hard because BYOND is, by default, a square-grid based system. But with a little work, you can set up your own grid system and move objects on the screen via pixel-movement (for example).