You might get different answers from different regions for this question. Literally, they mean the same thing, and all three can be used either literally or metaphorically. I'll add the following notes, though, based on my own experience: "Let go of it" is most often used literally. If two children are fighting over a toy, the parents might tell them both to "let go of it," meaning that they should stop grabbing the toy. "Let go" is the same, and is probably the more common form. If children are fighting over a toy, you can simply tell them, "Let go." ("Let go of it" is a little more emphatic.) "Let it go" is more often used metaphorically, in reference to something like a grudge, a regret, etc. If you complain all the time about how your ex-girlfriend left you, someone might tell you, "The relationship is over, so just let it go." The meaning is that you shouldn't keep thinking about it. You should mentally/emotionally "let go" of it.

Let it go and let go of it really mean the same thing. I can think of just sometimes where they are used in a slightly different way. Let it go is more of a command. You might tell it to someone that is dwelling on something too much or someone that you want to stop bothering you about something. Let go of it is more of a supportive thing you might tell someone to try to be helpful. For example. After an argument: Let it go! After a calm discussion over something someone is upset about: You know it’s important to let go of it. It’s a really fine distinction though and you could use either one in each case. Let go wouldn’t work without something more specific standing in for the it. Like let go of the anger.

You say, "Let it go." Almost no one in the US would say "Let go of it," though it's grammatically correct and would be completely understandable. It's just not vernacular for this expression.

very concise and useful answer. Bryannie, Thanks.

Let go/let go of it is usually used for something physical. For example; let go of the book. Let it go is often used in an emotional sense to mean stop thinking about it. For example; we already had that argument last week. Let it go.