A Nightmare on Elm Street 3: Dream Warriors
Neil Gordon was a selfish, lecherous, slightly middle-aged psychiatrist at Westin Hills who was particularly disliked by his young patients for trying to be friendly with them but blindly obeying the head doctor, Elizabeth Simms. Gordon was also a strong atheist. When he met Nancy Thompson, he did not believe her but attempted to put the moves on her just the same, but instead came to genuinely fall in love with her. He also gradually came to believe both her and in the existence of the supernatural, particularly after meeting the ghostly mother of Krueger. Along with Nancy, he helped form the "Dream Warriors".
Gordon also forced Nancy's now alcoholic father Donald, the man who killed Freddy Krueger, into revealing where he hid the corpse. Krueger had reached a particularly high level of power, and was able to animate his now skeletal body, which slew Donald and which Neil fought off before destroying it with holy water. Sadly, he was too late to save Nancy. He cried himself to sleep over her, presumably for the rest of his life.
Gordon never appeared in another film, but has appeared frequently in novels, short stories, and was the hero in many early, rejected drafts of the script for the 2003 film Freddy Vs Jason.
Neil Gordon suffers three very different fates in the various Nightmare on Elm Street-related comics across three companies.
In Marvel's short lived Black and White Freddy Krueger's Nightmare on Elm Street magazine, Gordon is not mentioned by name, but the deaths at Westin Hills are shown to have been declared a mass suicide. Presumably Gordon was held responsible for it all, and likely sued or imprisoned.
In Innovation's Nightmares on Elm Street series he helps the main characters. He is also brought into the dream world by the Dream Warriors, apparently for revenge at first for failing to save them, but then they reveal they merely want to give him a magic item to defeat Freddy. Gordon decides that life is meaningless without Nancy, so he gives up his body to be with her forever in the Dream Dimension. He then allows the ghost of Alice Johnson's boyfriend Dan, also father of her son, to take over his body since it would allow Dan to be reunited with Alice and become a respected psychiatrist who could provide for his family.
In Wildstorm's series Freddy Vs Jason Vs Ash: The Nightmare Warriors, he puts together the titular team along with Maggie Burroughs, initially as a support group for survivors of Freddy and Jason's rampages. He is slain by a now evil Maggie, but still is able to help defeat Krueger even in spirit form. He also briefly re-unites with Nancy, who promises she will always love him.