(covers information from several alternate timelines)
Externally, Betazoids were physically indistinguishable from Humans in every aspect but one: the irises of their eyes were completely black. They could breed with Humans, along with other humanoid races like Klingons and Tavnians. Betazoid iris coloration was present in half-Betazoid individuals such as Deanna Troi, but in those with less Betazoid blood such as Devinoni Ral and Walter Pierce (who were only ¼ Betazoid), normal Human eye coloration was possible. (TNG: "The Price") Betazoids had a gestation period of ten months. (TNG: "The Child")
Mature Betazoids could also suffer from Zanthi fever, which caused them to lose control over the projective aspect of their empathy. That could result in people around them acting as if they had experienced the same general emotional state as the affected Betazoid, though they were directed by their own subconscious desires, fears, and other emotions. (DS9: "Fascination")
Betazoids were natural telepaths, an ability centered in their paracortex, with psilosynine being a main neurotransmitter. (TNG: "Dark Page") Most developed their telepathic skill in adolescence, but a few were born with their telepathic abilities already active, such as Tam Elbrun. (TNG: "Tin Man") These individuals were almost always extremely talented and powerful in telepathic terms, but also unable to screen out the consistent noise of other people's minds, so they generally suffered mental problems of varying severity depending mostly on when the problem was diagnosed. On the other end of the scale were a few individuals who developed psionic abilities that were far below average for the species (for example, Lon Suder). Those Betazoids were barely able to sense even strong emotions (empaths) of other people, much less thoughts.
The common psionic abilities of Betazoids extended from sensing thoughts and/or emotions, over projecting thoughts and/or emotions, to manipulating the minds of others. (TNG: "The Price"; DS9: "Fascination") How capable they were in performing any of those feats depended somewhat on their genetically-defined psionic strength, their psionic training, (TNG: "Haven") their familiarity with the scanned being, their general mental and physical condition, and the species of the subject race. Betazoids can also feel the emotional capacity of animals, and thus were wary of getting too involved in the "passion of the beast" in situations in which they had to rely on an animal, like when riding a horse or keeping of various pets. (TNG: "Pen Pals") Betazoids also were able to read the emotions and thoughts of non-corporeal beings such as Nagilum, the energy vortex, or to gauge the mental prowess of beings such as Q. In essence a brain based "biology" was not necessary for a Betazoid to register. Other times they were totally unable to read corporeal creature's minds, such as Ferengi and Changelings. Data theorized that the reason they may not have been able to read Ferengi was the structure of their brains. Data himself was able to be read by Deanna Troi when his brother Lore used the emotion chip to transfer powerful emotions to him. One critical weakness of Betazoid telepathy/empathy was that in essence it operates much like any of the typical senses a person possesses (touch, taste, sight, hearing, etc.) that to lose one's abilities an individual may appear inanimate or unrealisitic. At one point, when Troi lost her empathy temporarily she commented that Will Riker was like a holodeck character to her, completely devoid of emotion, as if she had never experienced a lack of empathy from any sentient before. The Traveler was also not able to be read by Troi.
Interspecies reproduction involving Betazoids often affected the psionic abilities of the offspring – most commonly the children of such a union developed empathic abilities as their primary psionic talent, while their telepathic abilities, though existing, were rather below average for Betazoids. Usually the telepathy of those of partial Betazoid heritage, without extensive training, was limited to communication with other empaths or telepaths and full telepathic contact with emotionally very close persons (for example, an imzadi). All full Betazoids were unable to read the thoughts of Ferengi, Breen, Ullians, and Dopterians, but some half-Betazoids were occasionally successful in sensing the emotions of some of these species. Additionally, full Betazoids seemed to even be able to psionically influence some of these species. (TNG: "The Price", "Ménage à Troi", "Violations"; DS9: "The Forsaken", "Fascination")
Culture and tradition
Due to their telepathy, Betazoid culture largely progressed to the point where honesty was embraced by overall society, since the idea of hiding information among a race of telepaths would be functionally impossible; nonetheless, honest feedback was almost to a point considered rude by other cultures. Lwaxana Troi, on numerous occasions, commented on her befuddlement at the Human practice of fibbing to spare others' feelings or for politeness' sake. (TNG: "Haven", "Dark Page")
Betazoids had a complex hereditary nobility; prominent Betazoid diplomat Lwaxana Troi, for example, was "Daughter of the Fifth House, Holder of the Sacred Chalice of Rixx, and Heir to the Holy Rings of Betazed." Betazoid tradition had children genetically bonded to a future spouse. (TNG: "Haven")
At one time, it was fashionable for Betazoid women to wear elaborate wigs that caged small animals. The practice, which was cruel to the animals, was stopped when one (unknown) woman stood up against it. (TNG: "Half a Life")
A list of all appearances of Betazoids (excluding the regular appearances of Deanna Troi):
Originally, Gene Roddenberry conceived Betazoid females as having four breasts. He was persuaded not to use this idea by writer D.C. Fontana. (Star Trek - Where No One Has Gone Before paperback ed., p. 110)
The black coloration of a Betazoid's eye was achieved by the relevant performer wearing a pair of black contact lenses. The makeup team responsible for devising this method was essentially "trapped in not doing too much," in the words of Makeup Supervisor Michael Westmore. (Star Trek: The Magazine Volume 2, Issue 12, p. 26)
According to the novel Engines of Destiny, the Betazoids were known to the Borg as Species 1599.