How do I register a Javascript variable on the server side (backend) and access it on the client side (Javascript file), without a hidden field, Literal, etc.?
You can put a literal in the xml portion of the code and assign that literal some text:
myLiteral.Text = "";
This makes myVar globally available on the client side once it's rendered. You can also use the ClientScriptManager object to use Asp.Net to inject scripts and variables.