Java Edition:Offset Map
Maps are now designed to snap to a grid to make aligning them easy. However, this was not always the case.
Obtaining
Original Maps
From Beta 1.6 Test Build 3 through 12w32a (1.4.2 snapshot), the center of a map would be aligned on the location the map was crafted. This was changed in 12w34a, where maps would now align to a grid, regardless of crafting location. Therefore maps with center locations that do not fit the grid are all discontinued. These maps would always be at a 1:8 scale and could be zoomed out in later versions.[test] They could also be zoomed in from 15w34a through 15w44b, allowing for even more discontinued configurations.[test]
Zoomed Maps
From the time map zooming was introduced, 12w36a (1.4.2 snapshot), through 14w30c (1.8 snapshot), zooming out a map would not properly align it to a zoom grid. This was changed in 14w31a, which did align the map zooming grid. The location of the zoom was directly related to the place the map was zoomed out, similar to the way regular maps behaved prior to 12w34a. These maps could be zoomed in from 15w34a through 15w44b, allowing for more discontinued configurations.[test]