Here's what I've boiled it down to:

Code:
Public Class TestSig
    Dim MousePath As New Drawing2D.GraphicsPath()
    Dim xStart, yStart As Integer
    Dim CurrentPen As New Pen(Color.Black, 5.0!)

    Private Sub PictureBox1_MouseMove(ByVal sender As System.Object, ByVal e As System.Windows.Forms.MouseEventArgs) Handles PictureBox1.MouseMove
        'The below IfThen statement allows for the signee to start a new line
        If Math.Abs(xStart - e.X) < 30 AndAlso Math.Abs(yStart - e.Y) < 30 Then
            Me.MousePath.AddLine(xStart, yStart, e.X, e.Y)
        Else
            Me.MousePath.StartFigure()
        End If

        Me.PictureBox1.Invalidate()
        xStart = e.X
        yStart = e.Y
    End Sub

    Private Sub PictureBox1_Paint(ByVal sender As System.Object, ByVal e As System.Windows.Forms.PaintEventArgs) Handles PictureBox1.Paint
        e.Graphics.DrawPath(Me.CurrentPen, Me.MousePath)
    End Sub

    Private Sub btnClear_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnClear.Click
        'Clears the signature box
        Me.MousePath.Reset()
        Me.PictureBox1.Invalidate()
    End Sub

    Private Sub btnClose_Click(sender As System.Object, e As System.EventArgs) Handles btnClose.Click
        Me.Close()
    End Sub
End Class