The specifics depend completely on the universe, and in most universes the specifics aren't given. However, in virtually all universes, vampires are assumed to process their primary food source - blood - extremely efficiently. You never see a vampire sitting on a toilet for its intended purpose. Practically speaking, such details are neither good nor FCC-allowed TV, so if they're in a bathroom at all, it's to fix makeup or feed on some young girl they've lured to a bar restroom.
However, exactly why they gloss over this depends on the universe; in most universes they are just dead, so no beating heart, internal organs inactive, other than blood nothing's really happening in there. Other universes set vampires up as being "infected" by something; in Underworld it's a virus, it's not real clear in Blade, but vampires in those universes are "alive" at some biological level.
You also virtually never see a vampire HAVE to bathe for personal hygiene reasons. The only reason they would is to clean up and look presentable again after a particularly messy meal, or after burying themselves in the ground to sleep. How enjoyable a shower or bath (or dip in the pool) would be is universe-dependent; True Blood vamps like it, Twilight vamps can swim really well (and don't have to breathe) but getting wet is usually more necessity than enjoyment, and most other universes don't explore it much.
Other basic human needs (mainly air, food, sleep and sex) vary by universe:
True Blood: Vampires sleep during the day; they experience harmful but not fatal effects by staying awake. Vampires need to feed often, and apparently only some form of human blood (or synthetic substitute) will do, but vampires don't automatically infect their victims if they bite but don't kill them. To turn a human requires fully draining the victim, giving them some vampire blood, and THEN laying with them in the ground to complete the transformation (just swapping blood won't do it; that does, however, produce other effects). This is a workaround to the classic problem of why, if vampires exist and feed on humans, the human race didn't die out centuries ago. Vampires cannot starve to death, but are weakened by lack of food. Vampires apparently do not need to breathe except to speak. Intimate relations between vampires and mortals is completely possible (it's a major subplot of the entire series), and generally enjoyable for both sides (maybe with a certain masochism required of the human participant), and both humans and vampires have a general desire for it, but it can never result in offspring no matter the combination of vampire and mortal.
Underworld: Vampires sleep mainly to heal or recover strength; it doesn't seem to be a requisite to sleep during the day. Vampires must eat often (like every day or two), and when feeding on a human they must infect or kill, but blood of any kind, including that of livestock, is perfectly fine (though human blood tastes best). Vampires will not die without blood, but become extremely weak for lack of it. Vampires can hold their breath for an extremely long time, but do pant with exertion and so apparently do need to breathe (the first film also implies that they can drown). Sex is possible and enjoyable between various species, and there is at some level a desire for it. We only ever see immortals doing the deed, but it's probably possible between human and vampire, and it is definitely possible for immortals to get pregnant (it's part of the backstory of the first movie).
Twilight: Vampires don't sleep; they can't. Vampires must eat every couple of weeks or so, and the ones that feed on humans generally eat more often, every few days or even every night. It is apparently possible to starve to death, but it would take a very long time and the instinct to feed would become uncontrollable. Feeding on humans is infect-or-kill, and almost always the latter. Animal blood is acceptable for survival, but is an acquired taste to say the least. Vampires do not need to breathe, ever, but it is uncomfortable not to not do so. The Twilight universe is unique in that vampires are not burned by the sun. Sex is possible, enjoyable and generally desirable, but tricky between mortal and immortal; the vampire must first control their thirst for human blood, and second a vampire is so strong they could easily crush their human partner. A human woman can get pregnant from a vampire - that's a tricky situation too and a major subplot of Breaking Dawn - but vampire women are barren.
Blade: Vampires aren't shown sleeping, but are less active during the day for obvious reasons. Vampires must feed, only human blood will do, and until the cure is found halfway through the first movie, biting a human is infect-or-die in this universe (but it takes a while for a bitten victim to turn). For Blade himself (a "daywalker" hybrid), there is a serum that replaces blood; it's unknown if it would serve the same purpose for vampires. Breathing seems necessary at some level. Sex is probably possible and, behind the scenes, common between immortals; vampires generally want blood more than sex from humans. It appears impossible for either side to get pregnant from the other; Blade was born from a human mother who was infected while carrying him.
Buffy: Probably the closest to mythical vampires of the lot; they must sleep during the day, and must feed frequently (every day or two is typical). I'd thought it was human-exclusive, but apparently animal blood is fine too. Feeding on a human does not turn them; all the blood needs to be drained and then the human needs to ingest some of the vampire's blood. Apparently breathing is not strictly necessary, possibly even for speech. Sex is possible, but most vampires want humans for food more than sex, and Angel (the main "good" vampire in the series) cannot experience joy without losing himself to his demonic side. Pregnancy isn't explored AFAIK.
Interview With A Vampire (Anne Rice universe): Vampires sleep during the day, and desire to feed every day but can survive for quite some time without food. Blood is simply for survival; a vampire's strength is not determined by how well-fed they are. As turning a vampire happens by giving a drained victim vampire blood, biting in itself doesn't kill; the primary cause of death is blood loss. Animal blood is an acceptable but disgusting substitute. Breathing isn't covered AFAIK. Actual sexual intercourse is not possible, but vampires derive pleasure from a number of near-sexual acts, some more socially acceptable than others. As such, vampires can neither become pregnant nor get anyone pregnant.