As Yaacov Deane wrote in his answer, the Rambam puts great emphasis on a hygienical life and says that we must life healthy in order to serve our Creator. We must, according tot the Rambam, "accustom ourselves to things that are healthy and therapeutic".
In this vein, Rav Eliezer Melamed in his Peninei Halachah (Simchas HaBayis U'Virkhato, chapter 2:4) says that this all should be connected to Derech Eretz:
It should go without saying that derekh eretz includes maintaining personal hygiene and removing anything unsightly or likely to be off-putting. Getting rid of things which are off-putting is obligatory, while going above and beyond is admirable. This applies equally to both women and men.
It is even so important, that Rav Melamed says that showering during the Nine Days of Av (which Tisha B'Av concludes) is only permitted if a person feels literal pain when refraining from washing himself. If this is the case, Rav Melamed explains that a person can wash himself, although only with lukewarm water, in order to avoid pleasure from it.
The Lubavitcher Rebbe in his Igros Kodesh (vol. 3, p. 398) writes that one should be diligent in keeping a good and healthy body. This way, the unhealthiness will not serve as a hindrance to Torah study and the observance of mitzvos.
So, yes. One should take care of his personal hygiene. Not only for spiritual reasons, but also to prevent that his physical state (of illness) will prevent him from studying Torah and performing mitzvos (G-d forbid).
Edit: this Shabbos I've come across an fascinating piece from Rav Reuvain Grozovsky. In his Maamrei Rav Reuvain (p. 45) he says:
A person is obligated to honor his limbs and his body. It is part of the Mitzvah of Zeh Kaili v’anveihu since man was created b’Tzelem Elokim.