Most 2D tiled programs use a simple algorithm called "tweening" to show transitions between cells. It's a fake form of animation - it just briefly shows the same tile in between the two spots it's moving between. It can help make things look more natural.

Another trick for animating static tiles without real animation is to make tiles "bump" up and down as they move across. You can see this in Cardinal Quest and ToME4. It only needs a very subtle bump to look good, and it can make a world of difference for little effort.