documentclass[a4paper,12pt,icelandic]{report}
usepackage[toc,page]{appendix}
begin{document}
tableofcontents

chapter{Chapter 1}
section{Section 1.1}
subsection{Section 1.1.1}
chapter{Chapter 2}
section{Section 2.1}
subsection{Section 2.1.1}
appendix
chapter{Appendix A}
section{Appendix A.1}        % Do not show in table of content.
subsection{Appendix A.1.1}   % Do not show in table of content.
chapter{Appendix B}
section{Appendix B.1}        % Do not show in table of content.
section{Appendix B.2}        % Do not show in table of content.
end{document}

documentclass[a4paper,12pt,icelandic]{report}
usepackage[toc,page]{appendix}

**newcommand{nocontentsline}[3]{}
newcommand{tocless}[2]{bgroupletaddcontentsline=nocontentsline#1{#2}egroup}**

begin{document}
tableofcontents

chapter{Chapter 1}
**tocless**section{1}
**tocless**subsection{2}
chapter{Chapter 2}
**tocless**section{1}
**tocless**subsection{2}
**tocless**subsubsection{3}
appendix
chapter{Appendix A}
**tocless**section{Appendix A.1}        % Do not show in table of content.
**tocless**subsection{Appendix A.1.1}   % Do not show in table of content.
chapter{Appendix B}
**tocless**section{Appendix B.1}        % Do not show in table of content.
**tocless**section{Appendix B.2}        % Do not show in table of content.
end{document}