Originally the entities were directly influenced by key presses ie. pressing left would make the entity move one tile width to the left (Pressing SHIFT would make the entity sprint instead of walk) but this caused problems with the entity's animation and position if the entity began to sprint half way through moving.
I remember games like Flashback and Prince of Persia had a very distinct movement style where the entity would only begin to sprint when it reached the next tile. I tried to implement a system where the player would actually move onto the next tile instantly but the sprite would have an offset that would catch up to the entity eventually (and the entity would not process key presses until the sprite had caught up). This gave the right effect when moving left and right but it all started to fall apart when jumping / crouching / getting knocked back. Also I liked the way that (in Flashback) it was possible to press a button to draw your gun mid-step and the character would remember to do that when they reached the next tile.
Could anyone suggest a simpler way of achieving this kind of movement or point me to an existing example?