Are static class instances unique to a request or a server in ASP.NET?

On an ASP.NET website, are static classes unique to each web request, or are they instantiated whenever needed and GCed whenever the GC decides to disposed of them?

The reason I ask is because I’ve written some static classes before in C# and the behavior is different than I would have expected. I would have expected static classes to be unique to each request, but it doesn’t seem like that is the case.

If they are not unique to each request, is there a way to allow them to be?

UPDATE:
The answer driis gave me was exactly what I needed. I was already using a singleton class, however it was using a static instance and therefore was being shared between requests even if the users were different which in this case was a bad thing. Using HttpContext.Current.Items solves my problem perfectly. For anyone who stumbles upon this question in the future, here is my implementation, simplified and shortened so that it easy to understand the pattern:

using System.Collections;
using System.Web;

public class GloballyAccessibleClass
{
    private GloballyAccessibleClass() { }

    public static GloballyAccessibleClass Instance
    {
        get
        {
            IDictionary items = HttpContext.Current.Items;
            if(!items.Contains("TheInstance"))
            {
                items["TheInstance"] = new GloballyAccessibleClass();
            }
            return items["TheInstance"] as GloballyAccessibleClass;
        }
    }
}