Tellarites, Betazoids, Bolians
With ongoing problems with the Vulcans and Andorians, the Tellarites stepped up to the plate and helped form the Federation in the intervening years after the Romulan War. Nearly every Federation organization has a Tellarite member, and they make a substantial portion of the population of Earth. Despite, or possibly because of their "insulting" demeanor, a Tellarite ambassador is often used in almost every Federation negotiation, and are oddly seen as the most agreeable race.
The Betazoids come from an idyllic planet, and prior to coming in contact with the Yorktown, have never ventured off their planet or seen "space creatures." When they are discovered, they are the most telepathic species known. Their piercing black eyes often send chills into those who meet them. Despite their telepathy, Betazoids are naive to the ways of other species. Since they are telepathic, they have evolved very differentally culturally, and have very different morals, standards, and ethics.
The Bolians are an ultra-clean, almost obsessive-compulsive race from the planet Bolarus IX. Although their planet is officially considered habitable, there are amounts of poiso in the air which Bolians need to survive and most other humanoids die from after a few days. Because of this, Bolians often travel with specialized breathing material. When they travel, they have no qualms about insulting others' cleaning habits.