Is it possible to assign a base class object to a derived class reference with an explicit typecast?

No. A reference to a derived class must actually refer to an instance of the derived class (or null). Otherwise how would you expect it to behave?

For example:

object o = new object();
string s = (string) o;
int i = s.Length; // What can this sensibly do?

If you want to be able to convert an instance of the base type to the derived type, I suggest you write a method to create an appropriate derived type instance. Or look at your inheritance tree again and try to redesign so that you don't need to do this in the first place.

No, that's not possible since assigning it to a derived class reference would be like saying "Base class is a fully capable substitute for derived class, it can do everything the derived class can do", which is not true since derived classes in general offer more functionality than their base class (at least, that's the idea behind inheritance).

You could write a constructor in the derived class taking a base class object as parameter, copying the values.

Something like this:

public class Base {
    public int Data;

    public void DoStuff() {
        // Do stuff with data
    }
}

public class Derived : Base {
    public int OtherData;

    public Derived(Base b) {
        this.Data = b.Data;
        OtherData = 0; // default value
    }

    public void DoOtherStuff() {
        // Do some other stuff
    }
}

In that case you would copy the base object and get a fully functional derived class object with default values for derived members. This way you can also avoid the problem pointed out by Jon Skeet:

Base b = new Base();//base class
Derived d = new Derived();//derived class

b.DoStuff();    // OK
d.DoStuff();    // Also OK
b.DoOtherStuff();    // Won't work!
d.DoOtherStuff();    // OK

d = new Derived(b);  // Copy construct a Derived with values of b
d.DoOtherStuff();    // Now works!

I had this problem and solved it by adding a method that takes a type parameter and converts the current object into that type.

public TA As<TA>() where TA : Base
{
    var type = typeof (TA);
    var instance = Activator.CreateInstance(type);

     PropertyInfo[] properties = type.GetProperties();
     foreach (var property in properties)
     {
         property.SetValue(instance, property.GetValue(this, null), null);
     }

     return (TA)instance;
}

That means that you can use it in you code like this:

var base = new Base();
base.Data = 1;
var derived = base.As<Derived>();
Console.Write(derived.Data); // Would output 1