Basically everything Jan Valentine says, but highlights include:
Jan: Up Up! Down Down! Left Right Left Right! Bringing the motherfucking death by Konami! (pause) Ah I'm so fucking hard right now.
His hilarious call in the TV series to Integra and the Round Table:
Jan: And while you're waiting for us to kill you, we highly recommend pissing yourself! Followed by a course of praying to your impotent God! Then cowering in the corner and begging—always good—BUT IF YOU ACT NOW!—there's still time for an old-fashioned SUICIDE! Thank you London! We love you! Good night!
Jan: Come out and play little Hellsing. I promise its gonna be a lot of fun. We just want to torture you, kill you, maybe skullfuck your corpse a couple of times, burn the house to the ground, go home and masturbate okayyyyy.
From the same episode:
(Seras has just snuck up behind Jan and forced him down in a restraint hold, causing much complaint.)
Walter: Where did you learn that submission technique?
Seras: (over Jan's complaining) I AM a former police girl...
Meanwhile Jan is complaining about how he's supposed to be on top.
As if we didn't have enough moments from Janů
Jan: Now all that's left is to beat the shit out of a little girl and a bunch of old people.
Another Jan classic:
Jan: (smokes one of Integra's cigars) "Fuck,'' these are some fine cigars! Like, all bourgeois and shit. I mean, come on, that's just fucked up! People are starving in the world, and she's wasting money on this?!"
Speaking of the Valantine Brothers, at the end of every manga volume (except the first one) there are special comics depicting hilarious moments with them, like when they did a countdown for most popular Hellsing Character. They even put in characters that were never in Hellsing!
"Well! Just try and stop us, you self-proclaimed normal people!"
Not to mention the Harokken spirit talking to Seras Victoria.
"As a vampire, you were just a pathetic piece of shit. Now you're nothing but dog shit."
Seras defusing a potential brawl in the museum between Alucard and Anderson by guiding a tour group of Japanese tourists right past them ("Kochi desu yo!"). Alucard and Anderson just stand totally still, weapons drawn, as the tourists walk past, then:
Alucard: This is neither the time nor the place for a battle.
Anderson: Yeah, you may have a point there.
* both turn to leave*
Alucard: I'm leaving. Getting up in the daytime is so draining...
Anderson: (with a very kind smile) I must say this is an excellent museum. Perhaps next time I could bring some children from the orphanage?
In the manga, at least, the tourists are the "North Kasukabe Elderly Society" and mistake them for museum exhibits.
Elderly tourist: Ehh? Now why d'you suppose this priest has them sword-thingies?
Elderly tourist #2: Oh, I'll bet this is that "avant-garde" stuff! My grandkids love it.
Anderson and Alucard's dramatic brawl near the beginning of the fourth OVA.
Seras tries to join in and hit Anderson from behind, but it only takes a glare from him for her to stop dead in her tracks.
The manga, volume 11, Seras posing in red hat and coat: "Look! I'm imitating master!"
Schrodinger losing his copy of the mission briefing, having to read over the Captain's shoulder, and looking completely adorable.
The Wild Geese meeting Seras and Alucard for the first time. Hilarity ensues.
While sealed in her coffin during Volume 3, Seras has a vision of the spirit of the Harkonnen, who promises to support her and answer her questions:
Seras: O-okay, Mr. Spirit. There's just one thing I want to ask you! Everything's in the pits. Is the rest of my life going to be this unhappy?
Harkonnen: ... more or less.
Plus there's also that part of volume 2/OVA episode 2 with Seras snapping over the fact that, as a vampire, she would be sleeping in a coffin from now on. What really sent her screaming was how her normal bed was trashed and thrown away in favor of said coffin.
The scene where she has been locked in her coffin for the flight to Brazil (because apparently fledgling vampires can't survive crossing the ocean unprotected), screaming and yelling all the while until Alucard simply tells her to shut up. And she meekly does.
Let's just face it. Any time during the OVA when it undergoes an art shift, expect something funny to happen.
When one of the Major's subordinates expresses a desire to not go charging at Alucard's familiar army because it would needlessly sacrifice the lives of the troops, the Major pulls out a gun and shoots at the guy at point-blank range. And misses every shot, causing Doc to wonder how the Major got into the S.S. in the first place.
Also the scene with the Wild Geese Training session. When Seras attempted target practice, she snapped after hearing that she killed all hostages. Later, we see her having a spizfit over a lecherous song that Pip was singing.
We also see that in the credits of OVA 6, (with Magnolia playing) along with another funny scene involving ZORIN BLITZ of all people. A bunch of Millenium foot soldiers fight over a corpse that they plan on having for dinner, frustrating and irritating Zorin, and she slices the body in four separate scenes. This troper likes "hearing" (it was in a talk balloon so I use the word loosely) "Try not to make a scene at supper."
After you finish watching the epilogue for OVA 5, you're treated to a hilarious preview for OVA 6 with Alucard griping over having little to no screen time in the next two OVAs, and at the end, you're treated to a picture with... "Church of England Pro Wrestling." I snickered at the sight of it.
Near the end of the manga; Integra's exaggerated account of Lord Penwood'sHeroic Sacrifice. Could also be considered a Heartwarming Moment, as she's speaking to his grandson.
What's especially funny (and heartwarming in a weird way) is that she's basically telling the boy what he wants to humor him so that she can ask him for a new helicopter like she used to do with his grandfather.
In OVA 8, during the decisive battle between Alucard and Anderson, he suddenly switches back from his true form and starts lovingly and explicitly describing his new Jackal gun. Something about hearing him prattle off about it like a salesman with his Voice of the Legion just cracked this troper up.
In OVA 6, Integra cowing a member of the Iscariot Organization into lighting her cigar. The calm way she gives the command, the funny music that starts up, and the way she wiggles the cigar in her mouth as if to say "well, come on" makes it hilarious. To clarify, the Iscariot Organization hates the Hellsing Organization with a passion. And despite the soldier being armed, she obliges with great pain to her pride.
From there, she promptly browbeats the hit squad of trained assassins into escorting her back to Hellsing Manor. Father Anderson agrees to this, causing all of his comrades to promptly gape at him in pure disbelief...but having to go along with it, anyway!