Hide form instead of closing when close button clicked

Like so:

private void MyForm_FormClosing(object sender, FormClosingEventArgs e)
{
    if (e.CloseReason == CloseReason.UserClosing) 
    {
        e.Cancel = true;
        Hide();
    }
}

(via Tim Huffman)

I've commented in a previous answer but thought I'd provide my own. Based on your question this code is similar to the top answer but adds the feature another mentions:

private void Form1_FormClosing(object sender, FormClosingEventArgs e)
{
    if (e.CloseReason == CloseReason.UserClosing) 
    {
        e.Cancel = true;
        Hide();
    }
}

If the user is simply hitting the X in the window, the form hides; if anything else such as Task Manager, Application.Exit(), or Windows shutdown, the form is properly closed, since the return statement would be executed.

From MSDN:

To cancel the closure of a form, set the Cancel property of the FormClosingEventArgs passed to your event handler to true.

So cancel then hide.

If you want to use the show/hide method I've actually done this myself for a menu structure a game I've recently done... This is how I did it:

Create yourself a button and for what you'd like to do, for example a 'Next' button and match the following code to your program. For a next button in this example the code would be:

btnNext.Enabled = true; //This enabled the button obviously
this.Hide(); //Here is where the hiding of the form will happen when the button is clicked
Form newForm = new newForm(); //This creates a new instance object for the new form
CurrentForm.Hide(); //This hides the current form where you placed the button.

Here is a snippet of the code I used in my game to help you understand what I'm trying to explain:

    private void btnInst_Click(object sender, EventArgs e) 
    {
        btnInst.Enabled = true; //Enables the button to work
        this.Hide(); // Hides the current form
        Form Instructions = new Instructions(); //Instantiates a new instance form object 
        Instructions.Show(); //Shows the instance form created above
    }

So there is a show/hide method few lines of code, rather than doing a massive piece of code for such a simple task. I hope this helps to solve your problem.