Godzilla

Godzilla (ゴジラ) is a kaiju that did not appear in any Ultra series. However, one of his suits, the MosuGoji suit has made cameo appearances throughout some of the original series, such as the part one of the last episode of Ultraseven. Also, the monster Jirass is famous for having the same design as Godzilla, (but with a crest) due to the fact it was created from Godzilla suits borrowed from Toho Productions. Godzilla's suit was also used to create Gomess and his design was used for other monsters such as Earthtron. Along with Gamera, and of course, Ultraman himself, Godzilla is considered to be an icon of Japanese cinema.

Ultra Q
Kanegon's tail was compared to Godzilla's in Episode 15, "Kanegon's Cocoon".

Ultraseven
Godzilla's iconic roar can be heard in Dan's flashback montage to Seven's fights when his superior tells how the monsters he has fought have worn him down to nothing.

Ultraman Tiga
Godzilla's name along with Mothra's is mentioned in episode 49 of Ultraman Tiga.

Ultraman Max
Both Gamera and Godzilla figures are seen fighting in children's hands on Ultraman Max, "The Prophesy of Varaji". Before the epic vinyl battle could be continued though, the two children are interrupted by an attack on the city by the monster Antlar.

Trivia

 * Godzilla has indeed faced Ultraman in officially licensed media, although this happened in a fantasy soccer video game (Banpresto's Battle Soccer).
 * The Mosugoji suit is used to portray the monster Gomess in Ultra Q.
 * The suit is used again in Ultraman 1966 for the monster Jirass.
 * Bemular and Red King have edited Godzilla roars. Several other Ultra monsters used edited monster roars from Toho monsters, even into the Heisei era, such as Gatanozoa.
 * Since toys of Godzilla and Gamera appeared in Ultraman Max it is possible that they both existed in the Max Universe in the form of fictional characters in their respective franchises.
 * Near the end of Ultraseven, when Dan is remembering his past battles, Godzilla's roar can be heard. In some versions an image of Godzilla can be seen implying Seven fought with the famous monster, or as a cameo since Ultraseven's creator was an offscreen collaborator on the first Godzilla movie.
 * Both Godzilla and Ultraman are the creations of Eji Tsuburya, who served as the head of Toho's special effects. He also helped create several other famous Toho monsters like Mothra, Rodan, Baragon, and many more in Isiro Honda's franchise.
 * Haruo Nakajima, who has played as plenty of the Ultra Kaiju from Neronga, Gabora, and Jirass, is very famous for playing Godzilla since the original 1954 film all the way into Godzilla vs.Gigan in 1972. He has also played as other Toho monsters such Rodan, Varan, Baragon and Gaira (The Green Gargantua).
 * In the 1971 film "Godzilla vs. The Smog Monster", Godzilla at one point uses the Specium Ray pose.God_goji.jpg
 * A fan made Ultraseven manga features a form of Godzilla known as God Godzilla.  The image of Ultra kaiju bowing before God Godzilla is (in)famous enough to be commonly mistaken for an official Godzilla/Ultraman crossover.