Sempai-Kohai/Video Games

Dating Sim

The Tokimeki Memorial series, being a High School romance Dating Sim series, obviously loves this trope. Every flagship game of the series (save for Tokimeki Memorial 3) had a Kohai as a winnable Love Interest, and several side games introduced other non-winnable Kohai. However, winnable sempai weren't introduced until late in the series, the first one appearing in Tokimeki Memorial Girl's Side 2.

One set-type of double battle trainers in Pokémon is a pair of schoolgirls called "Sr. and Jr." ("Senpai and Kohai" in Japanese). The sempai is overly concerned with being a role model to the Kohai and the Kohai is overly concerned with impressing the sempai.

In Persona 4, Yosuke is surprised to find that the tough, rumored-to-be-in-a-biker-gang (he's not) Kanji is his kohai. He's also delighted when he finds out the cute and famous Rise is also his kohai when she attends the school. Unfortunately, Rise is more interested in your main character...
- One of the big differences between Personas 3 and 4 is that in Persona 3, the main character trio are the underclassmen (although your main character gives orders in battle because he is the most skilled in the use of his Persona) and sempais Mitsuru and Akihiko are calling the shots (to the point where they won't allow you to do any missions if both are not present), but in Persona 4 the main character trio (and later Yukiko as well) are the sempais and are in charge of the entire investigation team with the later members as their underclassman. The only 3rd year with a name in Persona 4 is Saki, who's killed off early on.
In Kingdom Hearts: Chain of Memories, Axel gives a hearty "ja ne sempai" to Vexen before he murders him in front of Sora. He's likely being snarky about it, though, because the other Organization members simply address their elders by name.

In Pokémon Mystery Dungeon: Explorers of Time/Darkness/Sky, Bidoof is delighted when your team joins the guild, since his seniority makes him your sempai, despite his own inexperience. One of Sky's Special Episodes reveals he even wished for a buddy or two to help mentor. Awww...

In Tsukihime, Shiki calls Ciel "Sempai" almost exclusively, even in his narration. Arihiko does the same. One point where you notice this is the first scene after Ciel wipes the school's memory of her; when Shiki asks Arihiko about her, he doesn't say "Who's that?", he says "Which sempai?"
Shirou is Sakura's sempai in Fate/stay night. He takes this responsibility seriously, and it makes him feel a bit awkward about being attracted to her. Rin is also her sempai, and that's unfortunate—it's one more edge that Sakura's sister has over her, one more reason to be bitter.
- Much like Shiki with Ciel, Sakura always refers to Shirou as "Sempai" (even when in the presense of other people who are also her Sempais, like Rin). Even in the HF True epilogue, where they've been in a relationship for several years and he's no longer even her Sempai, she still uses it (and Taiga calls her out on it).
From the Girls Love Visual Novel Sono Hanabira ni Kuchizuke wo, we have Yuuna as sempai and Nanami as kohai as part of a Schoolgirl Lesbians pairing. Kaede and Sara are also sempai and kohai but it isn't emphasized as much.