An otherwise unknown character uses the Dragon Balls to become a king. It is highly probable that the ramifications of this wish are still being felt to the present day, as the entire world is unified into one giant kingdom, with regional provinces dotting the globe, as shown in the King Piccolo Saga.
Oolong wishes for a pair of panties off a "hot babe" (though he just yelled the first thing that came to his mind as he was trying to stop Emperor Pilaf from making his own wish). Due to censorship issues, the English dubs changed this wish to "the world's most comfortable pair of ultra-soft underwear" (brought forth Oceanus Shenron in GT).
Bulma wishes that all the good people killed the day of the World Martial Arts Tournament to be revived. This resulted in Kibito being brought back to life along with the victims of the World Martial Arts Tournament (brought forth Naturon Shenron in GT). This wish also indirectly saved Shin and Gohan from death, due to their being healed by Kibito, who as aforementioned was able to do so due to being revived by this wish.
As they say their goodbyes to Tapion, Goku and friends mention that they will summon the dragon again to wish all the people back to life who died during the battle against Hirudegarn (this part of the conversation is only mentioned in the Japanese Version).
Future Pilaf wished to be young again, resulting in him, Shu and Mai to be turned back in infants (Future Mai later grows up into an adult and ends up in a relationship with Future Trunks). Future Piccolo died afterwards (thus making it the last wish granted by Future Shenron).
In Age 779, Towa and Mira prevent the Pilaf Gang from using the Dragon Ball's second wish and use the second wish to revive Cooler who is reconstructed into Meta-Cooler and takes part in Frieza's revenge.
In Age 850, Towa alters history by killing Shenron before Xeno Trunks can make the wish to summon the Future Warrior resulting in a massive time distortion in all the scroll capable of effecting the Time Nest & Conton City in Age 852. However Xeno Trunks manages to remember the correct history and finds the source of the change. As the Time Vault is on the verge of destroying itself the 2nd Future Warrior travels back to Age 850 to prevent Shenron's death and together with Xeno Trunks' past self defeats Towa allowing Xeno Trunks to make the wish correcting history.
In Age 852, at the behest of Tokitoki, Goku, and Beerus, Chronoa wishes for a feast that will leave everybody satisfied to celebrate the return of Tokitoki's Egg and the defeat of Towa and Mira in Age ???. According to Chronoa, Shenron created the feast using food from Earth.
Tekka and Pinich summon Shenron to wish for a tournament to determine the strongest in time and space. Due to the sheer nature of the wish, Shenron uses a lot of power to grant it and creates the Timespace Rift a warped dimension where different timelines and dimensions are connected allowing different people from different timelines to interact which is necessary for the Timespace Tournament that was created by their wish.
In the Timespace Rift in Area 4F near the ruins of his castle, Emperor Pilaf summons Shenron and wishes for a strong fighter to eliminate tournament fighters that had accosted the Pilaf Gang while they were searching for the Dragon Balls. Shenron grants the wish but due to Pilaf no specifying the nature of the fighter, Shenron summons the Legendary Super Saiyan Broly who rampages in search of Kakarot leading him to target Kid Goku. This leads Tekka's Team to summon Towa and Mira by opening time holes that combine into a large rift. Towa turns Broly into a Legendary Great Ape but he is defeated by Tekka's Team and blasted away by Beerus who was alerted to the Timespace Tournament due to Great Ape Broly's energy.