Because the start codon is translated into methionine, it clearly can not be part of the 5'-untranslated region, as @Johnny writes in his answer.
The more contentious question would be for the stop codons and the 3'-untranslated region. Then it really is a question of semantics. One might argue that as no amino acid is inserted in response to these codons, they are not translated. However if one considers the meaning of the word ‘translate’ and its application to the genetic code, a stop codon clearly is translated — it is read and translated into information which initiates the release of the nascent peptide from the ribosome.
And so in the Wikipedia entry on Untranslated Regions it (together with the start codon) is shown in the coding sequence, and not in the untranslated region. The annotations used by GenBank also include start and stop codons in the coding sequence (CDS in their annotations) — see, for example the annotation for this insulin precursor sequence.