In most internet sources it says Zeus, Hera, Poseidon, Demeter, Ares, Hermes, Hephaestus, Aphrodite, Athena, Apollo, and Artemis are always considered to be Olympians and either Hestia or Dionysus is added to the list. Hades is not considered an Olympian as he lives in the underworld. But in 'Mythology' by Edith Hamilton it says that Hades is an Olympian. Demeter and Dionysus are not included in the list and are referred to as 'two great gods of earth'. So which list of the 12 Olympians is correct?
There are many lists of the Twelve Olympians, and one can make an argument that any of the gods should or shouldn't be included. One of the most common lists is Zeus, Hera, Apollo, Artemis, Ares, Hermes, Poseidon, Demeter, Hephaestus, Aphrodite, Athena and Dionysus, and the Hestia gave up her seat in the Olympian throne room to Dionysus. This is the most popular list of the Twelve Olympians and is the one that is generally accepted by people who don't care too much. Although, really, why does it matter? There is no reason to group the Greek Gods by who had a throne on Mt. Olympus. I would argue Hades is much more important and powerful than Dionysus or Hephaestus. If we're grouping them by power level, Eros should really be on the list, considering many texts state that it is said that he is an entity feared by Zeus himself.
Tl;dr Usually the most common list has Hestia giving up her seat for Dionysus, but there is really no reason to group the Greek Gods this way. Arguments can be made for anyone's inclusion or exclusion on the list.