Monks and nuns generally take good care of their bodies so they may be better able to continue to share the dharma with those who may benefit. They keep good hygiene of their robes and living quarters to prevent disease and be healthy.
Here is an excerpt that gives a specific example of personal hygiene:
In the Anguttara Nikaya there is a short sutta in which the Buddha describes the benefits of using a tooth stick (dantakaṭṭha), the ancient Indian equivalent to our tooth brush. The advantages of regular brushing, the Buddha said, include that it is that it is good for the eyes, the breath does not have a bad smell, the taste buds are cleaned, bile and phlegm do not mix with the food, and food becomes more palatable (A.III,250).
Modern monks and nuns adapt the ancient teachings with regards to modern knowledge of hygiene. An example:
yo pana bhikkhu orenaddhamāsaṃ nahāyeyya aññatra samayā, pācittiyaṃ. tatthāyaṃ samayo, diyaḍḍho māso seso gimhānanti vassānassa paṭhamo māso iccete aḍḍhateyyamāsā uṇhasamaso, pariḷāhasamayo, gilānasamaso, kammasamayo, addhānagamanasamayo, vātavuṭṭhisamayo, ayaṃ tattha samayo.
Do not wash more than twice a month if the body is not dirty. Except than in exceptional situations, if a bhikkhu washes his body before half a month has elapsed since his previous washing, he commits a pācittiya.
These are the exceptional circumstances that permit a bhikkhu to wash:
during the hot season (period of two and a half months from the May new moon until the August full moon);
in case of illness, fever or any other medical reason.;
after having carried out a physical work that has caused sweating;
after having made a trip of a distance of at least half a yūjanā – between five and six kilometres;
when dirty (dust, mud, sand, excessive transpiration, etc.)
Attention: This rule only applies in the "majjhima desa" region of modern northern India, where the Buddha lived. In fact, bhikkhus living outside this region can freely wash, without committing a fault.
Discipline is for the sake of restraint,
restraint for the sake of freedom from remorse,
freedom from remorse for the sake of joy,
joy for the sake of rapture,
rapture for the sake of tranquillity,
tranquillity for the sake of pleasure,
pleasure for the sake of concentration,
concentration for the sake of knowledge
and vision of things as they are,
knowledge and vision of things as they are
for the sake of disenchantment,
disenchantment for the sake of release,
release for the sake of knowledge and vision of release,
knowledge and vision of release
for the sake of total unbinding without clinging.
-- Parivaara.XII.2 (BMC p.1)