How many types there are depends on what you mean by types.
There are 3 basic types.
The Sanguinarian who takes their life force/energy from blood.
The Psi Vampire who takes their life force/energy directly from the energy field created naturally by every living thing/naturally occuring phenomena.
The Hybrid Vampire who can use both of these methods to 'feed'.

However the Psi Vampire category can be split into several different types.

EMPATHIC Vampires feed on emotional life-force energies.
SEXUAL Vampires feed on the life-force energies generated from having sex, especially those generated at the moment of orgasm. (A female sexual Vampire is sometimes referred to as a succubus and a male sexual Vampire is sometimes referred to as an incubus). Sexual Vampires are also sometimes known as "TANTRIC" Vampires.
SOUL Vampires are able to feed directly off the energy of a person's soul. As a result Soul Vampires will sometimes gain some or all of the abilities, memories, thoughts and desires of the person they are feeding from, but usually only for a short time.
ELEMENTAL Vampires are Vampires that are able to feed on the life force energies of the elements; earth, wind, fire, and water.
Another method of feeding often considered a subcategory of elemental feeding is electrical feeding; the indirect feeding on energies in electrical fields and lightning.
There are those that say that Vampires who feed on life-force energies from plants and animals are also elemental Vampires. However, such Vampires will usually describe themselves as 'nature' Vampires.
ASTRAL Vampires are able to travel through the astral plane and feed off the life-force energies of other entities dwelling within, and/or materialize in astral form and feed off the life-force energies of people, usually while they are asleep.

Vampires who only use one method of feeding are referred to by the way they feed; Sanguinarian (Sang), Psi etc....
Vampires who are able to feed using all Psi methods are referred to as Eclectic Psi Vampires.
Vampires who are able to feed using all Psi methods and can also take their life force/energy from blood are referred to as Eclectic Hybrid Vampires.

This is the information I have.
I hope it helps.

Please note:
I have not included Role Play Vampires, who are simply humans with a love of all things Vampiric, and a love of behaving in the ways they believe a true Vampire might behave. Whilst their interest is flattering and mostly harmless, they are not really Vampires and so not included in the list above.
Also missing are the 'Immortal Vampires' who live forever, never changing, ageing or weakening in any way. The simple reason for this is that they do not exist. They are a fiction from books and movies and do not qualify for inclusion in the list above.

Come To Me.