Genos is very interested in learning how Saitama became strong as he is, tags along with Saitama often despite how many times Saitama says he can handle things alone, and later Genos decides to move in with Saitama....
Someone compiled a whole image◊ dedicated towards Genos serving under Saitama, which includes helping him by paying his rent, doing chores, cooking, being upset whenever someone disrespects his master, carrying his groceries, providing all the information Saitama would ever need on anything, going along with his silly shenanigans, buying an entire brand of Saitama Strips, writing every single habit and word his master speaks in his notebook, buying him drinks, and much more. To say that Genos is obsessed with Saitama is an understatement. Sonic seems to pick up on this as well, calling Genos a "clingy shithead" in the manga.
The anime somewhat adds in some additional scenes of interactions between them. One particular example being the climax of episode 7 where Genos sees negative comments accusing Saitama of causing the destruction of Z City online and rushes to the scene where he is being publicly humiliated by Tank Top Tiger and Black Hole. The episode ends with Genos telling Saitama that he will always be his follower no matter what people say about him, Saitama replies that he doesn't need to butter up things to make him feel better, and then turns back with a small smile of his face. The setting sun and soft guitar music in the background of this scene make it sound more like a Love Confession.
A bonus page by Murata reveals that Genos instructed the anime director on how to accurately portray Saitama, including the opening sequence's animation and lyrics, and shared all his notes on Saitama with a Wall of Text not unlike his own backstory exposition. The lyrics to the ending song are also oddly romantic and specific; "the person I love is so strong it worries me" is almost certainly about Saitama, and the only character that would make sense as the speaker given the anime context would be Genos. The line "I hope these feelings reach you" matches easily with a lot of Genos' internal monologing about his feelings concerning Saitama. Also worth noting is that in the Wall of Text the director is requested to not "miss out on his physical appeal".
In the second episode, when Saitama is standing naked in the street, Genos' eyes are wavering and he appears to be staring below the belt. Later, after being tested for the Hero's Association, Saitama is clearly looking at Genos' crotch (or rather, where it should be).
After their sparring match (which Saitama later refers to as "playing"), Saitama takes Genos out to eat. He gets worried when Amai Mask comes to talk to Genos, concerned that this is part of "newbie crushing" and that Genos might be injured. He's jealous when girls come up to talk to Genos afterward, and when they part ways at the end of the scene, Saitama frowns as soon as Genos turns away, and sad guitar music starts playing. Although he initially denies Genos' request to live with him, Saitama caves easily; Word of God confirms that Saitama hasn't used any of Genos' rent money.
Saitama is normally calm and appears emotionless. In the anime, he expresses the most amount of emotion around Genos, including irritation and worry when Genos is injured, always checking to make sure Genos is okay before proceeding to beat the Monster of the Week.
Genos fights with Sonic in order to keep Sonic from bothering a preoccupied Saitama. Sonic comments that Genos is a "clingy shithead" and that he appears to be "showing off" (Saitama wonders if he's gotten upgrades since the last time they "played together"). He prepares an attack that will almost certainly incapacitate Genos, but Saitama drags Genos out of the fight before he can get injured. Sonic accuses Saitama of getting soft for protecting Genos.
In the sixth OVA, Genos offers to defend Saitama in court. Saitama responds by being deeply offended that Genos doesn't believe he didn't kill Zombieman.
The anime director has stated that Genos isn't interested in (fan)girls, only in Saitama('s power), and that the only way to get Genos' attention to give him something for Valentine's day is to give Saitama something as well. Word of God also states that Saitama picked out the slippers and duster Genos is frequently drawn with.
In a recent drama CD, Genos is so inspired by Saitama's words that, having forgotten his notebook, he drills Saitama's words into his chest. In another drama CD, Saitama takes Genos to a festival to have fun, and actually spends money on him. The most notable one features the two trying to improve Saitama's reputation by changing his looks and attack name, which wouldn't be too out of the ordinary... if not for the fact that Genos paints on Saitama's naked body and puts cat ears on his head.
For a rare Les Yay example, Lily of the Three Section Staff from the Blizzard group often acts like she has Precocious Crush towards Fubuki. In the fifth OVA, Lily can be seen blushing and gushing over her hero when Fubuki saved Lily from one of Deep Sea King's leftover henchmen.
Garou and Metal Bat get shipped a surprising amount, for lots of Foe Yay. Shippers view their brawl as Belligerent Sexual Tension, and that Garou took mercy on Metal Bat out of both respect for Zenko and feelings for his opponent. It helps that they're both quite handsome, around the same age, love fighting, and have soft-spots for kids.