I feel I have to add my two cents here in defence of monastics.
First, no two monks/nuns are the same. They all have different rules to follow which are fine tuned for them by their spiritual guide depending on what they are capable of. This means that some do shower and some don't. A lot of concessions are made for new monks and nuns today because they are simply not prepared for the hardship involved right at the start. People who became monks/nuns during the depression or following one of the wars or simply during a time when living conditions were a lot more simple and basic were already used to such spartan living conditions, not so today.
Second, as my lovely wife pointed out to me, monks and nuns eat no meat and have a much simpler and healthier diet overall. As such their bodies do not produce the same kinds of odours we meat eaters produce.
Thirdly, they do not perspire nearly as much, though this is probably more to do with God's grace than anything. Andonis from mo'nachos.net told me that he was put to work helping in the ekthesi, the monastry shop, bringing boxes of books/icons/incense etc from the storeroom. He was wearing light trousers and a short sleeve shirt and was sweating profusely in the heat. The monks, however, were not even breaking a sweat despite the fact that they were all wearing a lot more including the rasso.
Fourth and most importantly, there is the action of God's grace. Anastasios said that being smelly doesn't make you holy, however I believe the converse is true, being holy makes you smell of sweetness. I don't know quite how to explain it. When a person attains to Christ in this life, the corrupt flesh of this fallen world is transformed by God's grace into something holy and pleasing. Thus instead of fouls smells you have sweet aromas. The bodies of many saints remain incorrupt and at the very least sweet smelling, none of them giving off the usual foul stench of death and decay. I remember reading of Mother Gavrilla, when working in the leper colony cutting the rotten flesh from around the sores of the patients she treated, God blessed her work by transforming the stench into a sweet smell.
In the monastries, they do take asceticism to extremes because they are striving for perfection and they live in an environment which supports this effort. We who live in the world cannot go to the same extremes because we would draw undue attention to ourselves. Even during the strictest of fasts, we should still wash regularly to keep our efforts in secret.
John the unwashed (because the water was cut off this morning due to pipe repairs. No warning either