"Forever Red" from Power Rangers: Wild Force includes characters from 9 shows with speaking roles

To commemorate the 10th anniversary of the Power Rangers franchise, the episode "Forever Red" of Power Rangers: Wild Force featured Red Rangers from every Power Rangers TV show to date teaming up to fight an enemy. Every one of them has speaking roles.

• Jason Lee Scott of Mighty Morphin Power Rangers
• Aurico of Mighty Morphin Alien Rangers*
• Tommy Oliver of Power Rangers: Zeo
• T.J. Johnson of Power Rangers: Turbo
• Andros of Power Rangers: In Space
• Leo Corbett of Power Rangers: Lost Galaxy
• Carter Grayson of Power Rangers: Lightspeed Rescue
• Wesley Collins and Eric Myers of Power Rangers: Time Force
• Cole Evans of Power Rangers: Wild Force

_{* Although some debate whether Mighty Morphin Alien Rangers counts as a show because it technically took place at the end of Mighty Morphin Power Rangers Season 3, it had a different opening theme and Wikipedia classifies it as its own series.}

"The Space Pirates Appear" from Kaizoku Sentai Gokaiger includes characters from 35 shows (without speaking roles)

Most of the characters just give a unified "hijah!" during an amazing fight scene in which nearly 200 Super Sentai Rangers fight an overwhelming army. Teams from all previous 34 series were present in this battle, with the titular Kaizoku Sentai Gokaiger appearing later in the episode.

The American version of this battle was shown in the Power Rangers: Super Megaforce final episode, "Legendary Battle", but since Power Rangers has had fewer seasons, only characters from 16 shows appeared, again with most only speaking by giving a unified battle cry.

_{In case you didn't know, Power Rangers gets its fight scene footage from Super Sentai and films new footage in between of English-speaking actors.}

Theatrical movies with TV show characters

The question only asked for TV show episodes that had characters from different shows, but there were a few theatrical movies in the Super Sentai franchise that with many actors from different shows.

Gokaiger Goseiger Super Sentai 199 Hero Great Battle includes characters from all 35 Super Sentai shows, with characters from 18 of them having speaking roles

The battle in "The Space Pirates Appear" from Kaizoku Sentai Gokaiger is revisited in this movie, with the first 34 Super Sentai teams at that point making an appearance, and the rest of the film focuses on the Gokaigers. The following characters from different shows have speaking roles:

• Tsuyoshi Kaijo of Himitsu Sentai Gorenger
• Sokichi Banba of J.A.K.Q. Dengekitai
• Daigoro Oume of Denshi Sentai Denziman
• Kanpei Kuroda of Dai Sentai Goggle V
• Rei Tachibana of Kagaku Sentai Dynaman
• Shirou Gou of Choudenshi Bioman
• Riki Honoo of Kousoku Sentai Turboranger
• Ryo of the Heavenly Fire Star of Gosei Sentai Dairanger
• Signalman of Gekisou Sentai Carranger
• Hyuuga of Seijuu Sentai Gingaman
• Umeko Kodou, Doggie Kruger, and Swan Shiratori of Tokusou Sentai Dekaranger
• Miyuki Ozu and Heavenly Saint Blagel of Mahou Sentai Magiranger
• Mele and Rio of Juken Sentai Gekiranger
• Satoru Akashi and Great Sword Man Zubaan of GoGo Sentai Boukenger
• Saki Rouyama of Engine Sentai Go-Onger
• Chiaki Tani, Genta Umemori, and Kaoru Shiba of Samurai Sentai Shinkenger
• All main characters of Tensou Sentai Goseiger
• All main characters of Kaizoku Sentai Gokaiger

Honorable Mention: Kaizoku Sentai Gokaiger vs. Space Sheriff Gavan: The Movie includes a single actor playing characters from three different shows

Along with speaking roles from characters of Kaizoku Sentai Gokaiger and Tokumei Sentai Go-Busters, this crossover movie contains a single actor, Kenji Ohba, reprising his roles from three different TV shows:

• Shirou Akebono of Battle Fever J
• Retsu Ichijouji of Space Sheriff Gavan (not a Super Sentai show)
• Daigoro Oume of Denshi Sentai Denziman