If you actually want examples that you could physically see proof of diffusion, than you would need some kind of physical characteristic to trace (usually color).
I suppose an example of a gases diffusing would be HCl and NH3, which is a common demonstration in chemistry lab. One soaks two cotton balls in each solution and places both of them at the ends of a clear tube. Both gases are colorless and as they diffuse through the air and through the tube towards the other gas, they react to form solid NH4Cl which will appear as a white cloud. If diffusion did not occur, you would not see this reaction.
A liquid diffusing through a liquid is a bit easier and the example I have can be done readily at home. Simply take a container of water (a cup) and drop a drop of food coloring. Over time, you'll see that the single drop has diffused to throughout the water.
Hope this helps :)