I have just reset all settings and preferences on my Illustrator to try and fix this bug, however it's not worked.
Whenever I try to move an item, Illutrator automatically adds 0.5px to the X and Y values.
This means it's unbelievably time consuming having to change every number as components never line up.
Am I missing something or is this a bug?
Any Snap to options active in your View menu?
Snap to Pixel/Point/Glyph are active, however even when these are disabled the issue is still present.
Looks caused by snap to pixel.
How do you move an item?
What is the Keyboard increment in your preferences?
Does it happen in new documents based on a print or Art & Illustration preset?
Is it also happening in any other/new document, rather than in a specific one?
If only in one document, you may be able to copy the artwork in its entirety/in parts/in part to a new document.
Try deselecting Use Preview Bounds in Preferences.
Or you may need to get rid of alignment to the Pixel Grid.
From CC 2017 on, you can see the options and behaviour here:
For earlier versions, you may select everything and then untick Align to Pixel Grid in the Transform palette, and also untick Align New Objects to Pixel Grid in the flyout options. It is crucial that the box is completely unticked, not just a - which also counts as ticked.
It may be noted that even if Align to Pixel Grid is unticked with all objects selected, as long as Align New Objects to Pixel Grid is ticked the creation of new objects will result in those new objects being aligned, even when they are created from existing objects as may happen with Pathfinder operations.
You may avoid document types with that as default (RGB for web and the like) or change the default for such documents.
Apologizing for possible dead links below.
Here is an exquisite screenshot made by Ton in the first post for older versions:
And here is an exquisite screenshot by Isa in post #3:
You may also see the screenshots by Tony in post #3 here: