This page about all Bender's main relationships in the series including those with his family members, friends and romantic partners:
Bender's Mom: Bender's Mom is a robotic arm located at one of the factories run by Mom's Friendly Robot Company she sends Bender Xmas Cards every year. According to Bender she is a religious fundamentalist and never told her son about robot reproduction. Bender also inherited his impressive arm control abilities from her. Bender does not visit or spend much time with her often, but does hold a soft spot for her expressing affection on getting a picture of her.
Bender's Father- Not much is known about Bender's late father, he of course originates from a factory under Mom's Friendly Robot Company. He was tragically killed by a giant can opener- which made Bender develop a phobia of them.
Flexo- Flexo is an estranged twin brother of Bender, with both of them having the same parents and being manufactured in the same factory. The two have crossed paths a few times but are overall not close to each other. Bender once dated Flexo's ex-wife Angelyne.
Vladimir- Vladimir is Bender's rich late uncle. In the episode, The Honking, Vladimir's will was read at his funeral which revealed that he wanted his nephew, Bender to inherit his home, Thermostadt Castle. This showed that Vladimir must have favored Bender especially (to give his home to him instead of his own children). Overall not much is known about Bender and Vladimir's relationship, but they appear to have gotten along quite well.
Carol Miller/Mom- Bender and all of the other robots created under Mom's Friendly Robot Company, hold Carol Miller in high regard and treat her as a mother figure, as it was her company that allowed all of them to be created. In the episode Mother's Day, Bender gave Mom several gifts and a talking card that according to himself he spent his own money on. Miller also acts nice to her robots, and presents herself as a caring, harmless and nurturing motherly figure to them in public but this is a deception and she actually sees them as expendable and her personal property. The narcissistic, egotistical and selfish Mom, no matter how great her robots become, will always see them as made to serve her and make her money. Despite being nearly killed by Mom's Killbots and controlled by her to rebel against people Bender is oblivious to her true nature and still treats her like his mother, because he was programmed to.
Phillip J. Fry- Fry and Bender are loyal best friends despite Bender's misanthropy. Fry helped Bender see life in a different light and lead him to a permanent job at Planet Express. Fry and Bender would shortly after befriending, move in to live with each other in Robot Arms Apartments as roommates. It is thanks to Fry that Bender decided not to end his life. Though Bender can be rough, tough and playful with Fry and sometimes lets him down, Bender does deep down care about Fry and is willing to do anything in his capabilities to make sure Fry is safe and happy. Whilst Fry is a kind, supportive and forgiving companion.