Halfbreed Saiyans look like Saiyans, who look like Humans with monkey tails. Even though they are only part Saiyan, Halfbreeds are considerably more powerful than either pure Saiyans or pure Humans alone. Gohan turns Super Saiyan when he is only 11, Goten does so at 6 and Trunks at 7. Goku, a pure Saiyan, doesn't reach the level until he is well into adulthood, likewise with Vegeta, the prince of all Saiyans.
Like the Saiyans, a Halfbreed will turn into a giant Oozaru when they are exposed to moonlight while they still have their tail. Chopping the tail off will stop this from happening.
List of Halfbreed Saiyans
It should be noted that Goku Jr and Vegeta Jr only appear in one of the Dragon Ball GT special movies, and that they are descendants of Vegeta and Goku. Goku Jr is the grandson of Pan.