Firo tends to serve as the designated Straight Man in Baccano!. Typically, he has to deal with Isaac and Miria's shenanigans, but other (usually profoundly violent) lunatics are happy to fill the role when the two aren't available.
In CLANNAD, Tomoya often takes the role of the "Straight Man" in regards to pranking other characters, particularly Sunohara.
Natsuki plays this role in Chronicles of the Going Home Club. Her clubmates often say or do extremely unusual things, such as fighting bears, being so absurdly rich to the point that spending money for them is the same as running tap water, or wanting to try eating the ice cream stuck on a lid as being the best part of it, only to then buy a popsicle instead.
Piccolo from Dragon Ball Z certainly seems to fall into this role, particularly when Gotenks is involved.
Excel Saga: Watanabe are Matsuya are the straight men for the somewhat hyperactive Casanova Wannabe Iwata, and, arguably, Sumiyoshi acts like this for all three of them when Watanabe and Matsuya are of the Only Sane Man. Excel and Hyatt play Straight Woman to each other, as both have their bizzare quirks that rarely overlap, and to Il Palazzo, who is the Comically Serious.
Shimura Shinpachi in Gintama. It's outright stated by the narrator during Shinpachi's very first appearance onscreen.
There's almost always a straight man on the scene. If Shinpachi is preoccupied or absent, somebody else typically ends up filling the role in his place.
Chapter 326 pokes fun at this. Shinpachi and Hijikata find themselves in a world where two years have passed and everyone changed. Shinpachi wonders if they are being punished because they have been neglecting their duties as a straight man.
Haré from Haré+Guu plays this role for pretty much everyone in the series.
In Nerima Daikon Brothers, the very sedate Ichiro typically plays the straight man for the other two members of the group — although he has some of his own strange quirks.
Often, Zoro of One Piece is this to Luffy and even Sanji at times.
Almost everyone in the entire crew (except Luffy) has moments of being the straight man, but none of them are always was the straight man (not even Robin, who has probably the darkest sense of humor out of all of them).
Liquid from Papuwa, as well as Shintaro from the original series.
Problem Children Are Coming from Another World, Aren't They? has Kurousagi to the problem children, and occasionally other characters like Shiroyashi. Kurousagi is constantly trying to curb their goofball antics, and they constantly twist her words or plainly contradict her in favour of fun, usually at her expense.
Fuyuki Hinata from Sgt. Frog. He exhibits great patience and friendship towards the Keronians, and is often the voice of reason and manages to diffuse conflicts, whereas his older sister Natsumi is blatantly racist to the point where she is hated by many fans.
Dororo could also be considered a straight man, seeing as he is always at odds with Keroro over his plans to take over Earth, since Dororo is basically a tree-hugging hippie.
In Slayers, Zelgadis is the straight man for Amelia. Lina and Gourry, meanwhile, are a fluid pair, each one switching between straight man and comic role depending on the routine.
Gourry is usually straight man when Lina is plotting something or when she goes on one of her rampages of destruction. Lina is usually straight man when thickheaded Gourry tries to understand something.
Also, Gourry frequently tries to abandon the straight man role by straight-up telling jokes. These are always awful, and leave Lina exasperated. Gourry ends up disheartened, though ironically, doing this puts him in the comic role like he wanted.
My Monster Secret: The role bounces around a bit depending on which characters are in focus. Asahi and, to a lesser extent, Mikan tend to be the ones who play the part most often, though there are plenty of cases where they're Not So Above It All. Later on, Asahi's sister Mei proves that this might run in their family.