if you want the button and the Text box to keep track of the value its self try this.
Code:
private void segbutton_Click(object sender, EventArgs e)
{
// if the box is empty set seg to 0 other wise convert contents of text box to an int32 and set seg
// will be empty on first post back of form if not set at client side
int seg = String.IsNullOrEmpty( segtextBox.Text.Trim() ) ? 0 : Convert.ToInt32(segtextBox.Text.Trim());
segtextBox.Text = (seg+=1).ToString();
}