Other characters: Neutral or minor characters, and characters never given names.

Shen-Long
Shen-Long is the Dragon God. When all 7 Dragon Balls are brought together and the words "Ide yo, Doragon!" (Come out Dragon) are said, he comes out and grants the first wish asked of him. Shen-long can never grant the same wish twice; this became a big deal in the second series, as hero deaths were fairly common and nobody could be revived twice. For the most part, bringing back dead people is the usual wish, too. After Dende becomes the Earth's Kami, he powers up the dragon Balls so they can grant more wishes.
Porunga
This is the Namek-sei equivalent of Shen-long. He looks much different than Shen-long. He is much bigger and is sort of like the upper torso of a dragon-like humanoid, rather than a long Eastern Dragon. Porunga's powers differ slightly than Shen-long' s; he cannot bring large numbers of people back from the dead at once, but he can grant three wishes and can grant the same wish more than once. Later Porunga gains a power-up so that he can bring large numbers of people back to life in one wish.
The Announcer/Judge at the Tenkaichi-Budokai
The Announcer of the Tenkaichi-Budokai has been the same for all five in the entire series. He's a man with blond hair and sunglasses. After the second Budokai he grew a moustache. He considers the Tenkaichi-Budokai "his;" he gets really distraught at having it destroyed and at having nothing but boring fights held there. That's why he's so happy at having Gohan and the others compete there after 17 years of "boring" Budokais.
The people of Jingle village
When Gokuu's plane crashed in the snowy regions and knocked him unconscious, a girl from Jingle village, Snow saved him from freezing to death. She told him about the imprisoned elder in Muscle tower, thus starting Gokuu's first major encounter with the Re d Ribbon Army. While most of the people from the village remain unnamed they were an important part of the story line for a while. We get to see them all again at the very end of the second series. We don't actually get to learn Snow's name until then either.
Brief and Bulma's mother
Brief is Bulma's father, but we never learn Bulma's mother's name. Brief is the head of the Capsule Corporation, the company that makes the Hoipoi capsules that turn into big things like cars and houses. Both Brief and Bulma's mother make appearances every once in a while throughout both DB and DBZ, but aren't really major characters. Occasionally Brief will make some important invention, though.
Uranai-no-baba's champions
If you can't pay Uranai-no-baba's fee for seeing the future, you have to fight her champions. They are: Dracula Man, a vampire with boxing gloves who can turn into a bat and hates garlic and crosses (of course), Suke, an invisible man, Mira, a mummy that can use his bandages as a tool, and Akkuman, a devil-man who can fly and can use the evil in people's hearts to make them explode. We never learn who her fifth champion was usually but when Gokuu came it was Son Gohan, his adopted grandfather.
The Kokuoo (King)
An anthropomorphic animal of some sort he rules the land and lives in King Castle. When Piccolo-Daimao revived, the Kokuoo became a primary target. Piccolo-Daimao forced the Kokuoo to give the country to him, and thus took over the world until he could be defeated.
The Saichoryo(s) of Namek-sei
The Saichoryo of Namek-sei is like Kami-sama; he created the Namek Dragon Balls, and they are bound to his life force. Therefore, if he dies, the Dragon Balls disappear. The first Saichoryo had the power to power-up people just through touch; he powered-up Kuririn, Gohan, and Dende this way. After he died, the elder of what was Dende's village, Muri, became the Saichoryo of the new Namek-sei.

Shapner and Ireza
Shapner and Ireza are two of Gohan's classmates. Shapner is a long-haired guy with a fairly big ego, and Ireza is a short-haired blond girl with a crush on Gohan. They never play a large role in the story but they do uncover Gohan's identity as Great Saiya-jin man at the Tenkaichi-Budokai.