The Bat Familiar will attack enemies, and as Alucard levels up the Bat's attack will become stronger. Also when Alucard morphs into a Bat, another Bat will show up after you level up, and eventually Alucard will have several Bats following him around when he morphs. The Bat Familiars will also shoot a fireball when the Alucard morphed bat shoots one.
To obtain the Bat Familiar you need the Bat Card, located in the Alchemy Laboratory.
The Demon Familiar pushes buttons in walls that Alucard cannot reach, which will open up new areas in the Abandoned Mine and Cave. As you level up the Demon will be equipped with Fire, Ice, Thunder, and Lightning Spears.
To obtain the Demon Familiar you need the Demon Card, located in the Abandoned Mine.
The primary use of the Faerie Familiar is for healing, but she also points out entrances to hidden rooms, and gives Alucard advice on getting through certain difficult areas of the castle.
To obtain the Faerie Familiar you need the Faerie Card, located in the Long Library.
The Ghost Familiar is very weak and does not help out much at all until it levels up. After it gets stronger it has the ability to Soul Steal, and also can drain enemies HP and give the HP to Alucard.
To obtain the Ghost Familiar you need the Ghost Card, located in the Castle Keep.
The strongest of the group, the Sword Familiar can provide powerful attacks but is rather slow at first. When reaching level 50 it can be used as a weapon.
To obtain the Sword Familiar you need the Sword Card, located in Olrox's Quarters.