Can one become a nazir today?
In principle, one can become a nazir today. This will obligate the person in all the laws of nazirus, i.e. avoiding all wine and grape products, and not cutting hair.
It is not generally recommended to become a nazir today, because one cannot offer the sacrifices that conclude the nezirus period, so that somebody who becomes a nazir will be doing so for life.
In addition, the opinion of the Raavad is that even a precondition of defilement is forbidden for a nazir, and not only becoming defile (with tumas meis), and this is another reason to avoid nezirus.
Therefore, we do not find (many) people taking on nezirus today.