In 2346, Rozhenko served aboard the Excelsior-class USS Intrepid under Captain Drew Deighan when the ship answered a Klingon distress call following the Romulan attack on the Khitomer outpost. In the wreckage of the outpost, Sergey discovered a young Klingon named Worf. Through an act of kindness, Sergey and Helena fostered Worf. (TNG: "Heart of Glory", "Sins of the Father")
After some time, they returned to Earth. Sergey occasionally took his sons camping in the Ural Mountains. (DS9: "Change of Heart") Worf eventually left his family to attend Starfleet Academy. The Rozhenkos continued to live out their retirement in the same dwelling for a number of years to follow. (TNG: "New Ground")
In 2367, the Rozhenkos visited the USS Enterprise-D while it was docked at Earth Station McKinley following its encounter with the Borg. They transported aboard from Earth Station Bobruisk. During their visit, they received a full tour of the Enterprise-D (excluding some areas due to repairs), and later both parents shared their concern and showed their support for Worf's recent discommendation following a conversation with Guinan. (TNG: "Family")
Later that year, Sergey and Helena met the Enterprise-D at Starbase 73 to take their grandson, Alexander, back to Earth. They intended to provide him with a home and a family following the death of his mother, K'Ehleyr, something Worf felt he could not provide on his own as he was both single and a career officer. (TNG: "Reunion")
By 2374, Alexander had decided to join the Klingon Defense Force. Sergey and Helena were not happy about the decision, most likely because of concerns over his safety and perhaps sensing that their grandson's motives had more to do with getting his father's attention then actually serving the empire. But, when they realized Alexander was determined to enlist, they supported him as they always had. (DS9: "Sons and Daughters")
"Don't call me sir. I used to work for a living."
- - Sergey Rozhenko, joking with Miles O'Brien
"So we walked into the school and we don't know what to expect. Is Worf hurt? Is he in some kind of trouble? The door opens and there is our little seven year old sitting on a chair and glaring across the room at five teenage boys, all of them with bloody noses."
"And then the principal looked up and said, please tell me he's an only child."
"We have taken enough of the Commander's time."
- - Sergey Rozhenko, Helena Rozhenko and Worf, discussing Worf's childhood with Geordi La Forge
"Mother, Father, I wish you would be a little more reserved while you are on board."
- - Worf
"I must bear my dishonour alone."
"That is not true."
- - Worf and Sergey Rozhenko
Sergey Rozhenko was played by actor Theodore Bikel.
The script for "Family" gives the pronunciation of Rozhenko's name as "sir-GAY rah-ZHEN-koh". It goes on to describe the character as being of Russian decent carrying himself with pride and dignity, "compact, barrel-chested... a retired Starfleet Chief growing old gracefully." 
The presence of Sergey and Helena Rozhenko in "Family" was of some concern to the production staff who felt Worf's parents might come across as comically "Jewish". Michael Piller ultimately felt the finished episode "trod the line" of universal humor. (Star Trek: The Next Generation Companion, p.143)
When Rozhenko meets Chief O'Brien for the first time he identifies him as a chief petty officer. At the time the episode was produced, this was considered a writing error as O'Brien wore the two solid pips of a lieutenant. The "Chief" in O'Brien's title was intended to refer to his position as transport chief, not his rank. Ultimately, O'Brien's rank was retconned when Deep Space Nine premiered so the line is now retroactively correct. (Star Trek: The Next Generation Companion, p.143)
Sergey Rozhenko appears in the Star Trek: The Lost Era novel The Art of the Impossible, which tells the story of Worf's rescue and adoption by him and his wife, Helena, following the massacre at Khitomer, in 2346.