is the a C# equivalent to TextBox(i).Text =

[TheGreatCthulhu]

NullReferenceException:

The line:

TextBox[] textBoxArray = new TextBox[10];

creates a new, empty array of TextBox-es.

When you write "textBoxArray[i]", you are accessing an element of the array, however, all elements are null so far (equivalent to Nothing in VB.NET).
For "textBoxArray[i].Text = "whatever";" to be able to work, "textBoxArray[i]" has to return an existing TextBox object.
The statement is basically equivalent to textBoxAtLocation_i.Text = "whatever";.

So, you need to put all the textboxes in the array before you can set the Text property.
Wich brings me to your other question.

My example:
I forgot something. The Add() method expects a TextBox, yet the textboxes it gets are all treated as Control-s (Control is on the inheritance chain of TextBox). They need to be type-cast back to TextBox.

// Assuming that all the textboxes are direct children to the containing form 
// (i.e. some of them aren't on a special panel or some other container subelement)
List<TextBox> list = new List<TextBox>();
foreach(Control c in this.Controls)
{
    //checks for a more specific type of c
    if(c is TextBox)
        list.Add((TextBox)c);
}

// now, assuming you have a TextBox[] member variable called _textBoxes
_textBoxes = list.ToArray();

That should do the trick.
Note: You want to do this only once - at the start (assuming you're not adding more textboxes at runtime). Maybe in the constructor of your form.
For this to work, the _textBoxes array (or textBoxArray in your example needs to be a member field of the Form1 class, so that it can be acessible to any of its methods.
Also, it's even more convenient to use a list instead of an array, as you can dynamically add and remove elements form it. Just use it's Count property in for-loops, or simply use foreach.