Increments for moving objects gets messed up? Sometimes when I am in a project, somehow the increments (I guess this is what you call it) for moving objects gets messed up or reversed? Like see here:

This is what normally happens:



This is what happens when it gets glitched (it's like you are holding Control when moving it, but I'm not)



How do I fix this when it happens? I want it to just move like it does by default. If I wanted to move it that way, I would just hold down Control when doing so!

I hope this made sense. Thank you!
You've accidentally enabled Snapping during transform (the little magnet icon) with Increment setting. So it's automatically trying to snap to the "grid" of the world when you move it around.
It's a super handy feature when modeling. 

You can read more here Transform Snapping

Hope this clears it up. I highly recommend reading up on this feature and playing around with it, it's SUPER useful when polymodeling and moving things around.