Joss Whedon (the creator) has created his own set of rules and regulations that define vampires. Though of course there are certain exceptions.... When killed a vampire turns to ash. The exception was the Master.
Vamps can be killed by fire.
Vamps can be killed by DIRECT sunlight. They don't burst into ashes immediately, they kind of smolder a little, burst into flames and then explode into ash.
Vamps die when decapitated.
Vamps die when staked through the heart with wood.
Holy water burns their flesh, but Buffy killed vampire Zachary Kralik by tricking him to drink holy water.It burned him from the inside ou.
They cannot transform into bats or wolves or any such thing. That was until Dracula showed up in season 5. Dracular posses special powers so he could lure people to him, and do neat tricks.
They do not need to sleep in a bed of the dirt from their native land. Although, Dracula did. Nor do they sleep in coffins.
They cast no reflection, but they do cast shadows. They can be photographed and videotaped.
While they do not need to breathe to survive, many breathe to create the illusion of being human. When Buffy was drowned by the Master, Angel was unable to provide her with CPR.
Though vampires can enter churches, actual contact with consecrated earth causes them great suffering. Contact with crosses also burns their flesh.
When humans become vampires they lose their souls. This keeps them from feeling bad about killing all of the people they kill. We all know the exception to this rule is Angel.