Has there ever been an experiment performed that demonstrated a form of 'spatial memory' in a unicellular organism? I'm imagining something analogous to the classic 'rat in maze' experiments, but obviously on a much smaller scale. Possibly even something as simple as following a concentration gradient, but choosing to go either upstream or downstream based on some sort of prior reward in a similar circumstance.
To build on busukxuan's answer, there are a lot of single-celled organism responses that kind of resemble memory:
Slime mold uses an externalized spatial 'memory' to navigate in complex environments - essentially, a slime mold leaves behind a trail, which it then avoids, allowing it to avoid where it has traveled in the past.
If the amoeba Dictyostelium sees an increasing cAMP gradient, it will follow that gradient - and then be less sensitive to a reversal in the gradient: Cellular memory in eukaryotic chemotaxis
In fact, even bacteria have some memory - they can figure out whether or not they are going up a chemoattractant gradient by making a comparison with the signal they observed a few seconds ago: Temporal comparisons in bacterial chemotaxis