Is it necessary to explicitly remove event handlers in C#

In your case, everything is fine. It's the object which publishes the events which keeps the targets of the event handlers live. So if I have:

publisher.SomeEvent += target.DoSomething;

then publisher has a reference to target but not the other way round.

In your case, the publisher is going to be eligible for garbage collection (assuming there are no other references to it) so the fact that it's got a reference to the event handler targets is irrelevant.

The tricky case is when the publisher is long-lived but the subscribers don't want to be - in that case you need to unsubscribe the handlers. For example, suppose you have some data transfer service which lets you subscribe to asynchronous notifications about bandwidth changes, and the transfer service object is long-lived. If we do this:

BandwidthUI ui = new BandwidthUI();
transferService.BandwidthChanged += ui.HandleBandwidthChange;
// Suppose this blocks until the transfer is complete
transferService.Transfer(source, destination);
// We now have to unsusbcribe from the event
transferService.BandwidthChanged -= ui.HandleBandwidthChange;

(You'd actually want to use a finally block to make sure you don't leak the event handler.) If we didn't unsubscribe, then the BandwidthUI would live at least as long as the transfer service.

Personally I rarely come across this - usually if I subscribe to an event, the target of that event lives at least as long as the publisher - a form will last as long as the button which is on it, for example. It's worth knowing about this potential issue, but I think some people worry about it when they needn't, because they don't know which way round the references go.

EDIT: This is to answer Jonathan Dickinson's comment. Firstly, look at the docs for Delegate.Equals(object) which clearly give the equality behaviour.

Secondly, here's a short but complete program to show unsubscription working:

using System;

public class Publisher
{
    public event EventHandler Foo;

    public void RaiseFoo()
    {
        Console.WriteLine("Raising Foo");
        EventHandler handler = Foo;
        if (handler != null)
        {
            handler(this, EventArgs.Empty);
        }
        else
        {
            Console.WriteLine("No handlers");
        }
    }
}

public class Subscriber
{
    public void FooHandler(object sender, EventArgs e)
    {
        Console.WriteLine("Subscriber.FooHandler()");
    }
}

public class Test
{
    static void Main()
    {
         Publisher publisher = new Publisher();
         Subscriber subscriber = new Subscriber();
         publisher.Foo += subscriber.FooHandler;
         publisher.RaiseFoo();
         publisher.Foo -= subscriber.FooHandler;
         publisher.RaiseFoo();
    }
}

Results:

Raising Foo
Subscriber.FooHandler()
Raising Foo
No handlers

(Tested on Mono and .NET 3.5SP1.)

Further edit:

This is to prove that an event publisher can be collected while there are still references to a subscriber.

using System;

public class Publisher
{
    ~Publisher()
    {
        Console.WriteLine("~Publisher");
        Console.WriteLine("Foo==null ? {0}", Foo == null);
    }

    public event EventHandler Foo;
}

public class Subscriber
{
    ~Subscriber()
    {
        Console.WriteLine("~Subscriber");
    }

    public void FooHandler(object sender, EventArgs e) {}
}

public class Test
{
    static void Main()
    {
         Publisher publisher = new Publisher();
         Subscriber subscriber = new Subscriber();
         publisher.Foo += subscriber.FooHandler;

         Console.WriteLine("No more refs to publisher, "
             + "but subscriber is alive");
         GC.Collect();
         GC.WaitForPendingFinalizers();         

         Console.WriteLine("End of Main method. Subscriber is about to "
             + "become eligible for collection");
         GC.KeepAlive(subscriber);
    }
}

Results (in .NET 3.5SP1; Mono appears to behave slightly oddly here. Will look into that some time):

No more refs to publisher, but subscriber is alive
~Publisher
Foo==null ? False
End of Main method. Subscriber is about to become eligible for collection
~Subscriber

In your case, you are fine. I originally read your question backwards, that a subscriber was going out of scope, not the publisher. If the event publisher goes out of scope, then the references to the subscriber (not the subscriber itself, of course!) go with it and there is no need to explicitly remove them.

My original answer is below, about what happens if you create an event subscriber and let it go out of scope without unsubscribing. It does not apply to your question but I'll leave it in place for history.

If the class is still registered via event handlers, then it is still reachable. It is still a live object. A GC following an event graph will find it connected. Yes, you will want to explicitly remove the event handlers.

Just because the object is out of scope of its original allocation does not mean it is a candidate for GC. As long as a live reference remains, it is live.