Does anyone have any tips on how to actually improve a game’s graphics within the free Unity? I have seen so much amazing games made on Unity, however, they all seem to look a lot better than my projects. I will take any tips!
Thanks 
The only things Unity Pro adds are shadows and post-processing effects. Both powerful tools in their own right, but they aren’t everything.
What you can do with Unity Free is make good artistic use of what shaders you have. Writing shaders is a pursuit in its own right, but you should have enough to work with using Unity’s built-in shaders.
At this point it all comes down to artistic talent.
The way I started to discover what made games look so dramatically different was when I was messing with a test level in UDK. Even the simple blocks seemed to have prettier lighting than my simple blocks! But then I realized they’re not so simple; even the base building-blocks use a dull specular shader; hard to notice, but these little things make a big impact.
Dead-Eye Conner of course but as Nemox said improving a games Visuals will take many combination’s and efforts on your part and a lot of learning.
You can use the Beast Light Mapper as well as Light Probes but since you said you have Unity Free then a good way to do this is to setup multiple lights (no shadows needed) in the right way. This often means a combination of lights with a combination of settings.
You can and should use about 1-4 lights max in a scene - for example If I have a character I would place 3 lights on the scene, they could be 2 spot lights, 1 area light and attached to my camera is another light lets say a Directional light.
You can also use your packaging program to bake in lights.
So in other words there are ways for you but this can easily take a lot of time on your part. Experimentation is key.
Also the Right Shader’s are very important - my recommendation is Rim Light Normal Map Shaders or Just the Standard Rim Light - with the right settings they could create the Unique Look but powerful. to make one you can look here :
Another one I like myself is a modified Skin Shader for Unity 3. You can search for that but theirs a special way I used that to create a nice effect with the right combination’s. Once again that comes down to combination’s. The link I sent you is to a Shader Tutorial. Learn and Earn my friend ~!