PipxSeras is the One Canon Pairing of Hellsing. Despite the hints of romance caught between other characters (not to mention the romances extrapolated without any hints at all), they all fall short of this one. Pip and Seras are an item. Unfortunately, it doesn't last long.
Their relationship gets off to a rocky start. In the very beginning, Seras demonstrates the existence of vampires by flicking Pip into a wall; to her chagrin, a bruised and bleeding Pip brands her a freak. The tables turn quickly: Pip adjusts without much trouble and learns to send Seras running, through the power of dirty songs.
Pip is captain of the Hellsing troops, and that includes Seras; she accepts him grudgingly, as she's the one who has to train the Wild Geese to deal with vampires. The practice fields are a hot spot for a while ("What do you mean you can't hit a target from 500 meters?" "Well, your gun just blew up all the hostages!")
On missions where they have to work together, though, they develop a friendship; and Seras stops running away from Pip and starts retaliating. He's bringing out her backbone.
In the meantime, Pip looks beyond Seras' vampirism and sees her for what she is: a "good girl", the kind that it would be dishonorable not to protect. Seras brings out Pip's nobility. They're good for each other.
Before sending Seras off to play first-line-of-defense in Zorin Blitz's assault on the Hellsing mansion, Pip tries to steal a kiss. She yells at him, but when Seras leaves she's smiling.
The attack brings catastrophe: most of the Wild Geese are killed, and Seras is badly wounded in a duel with Zorin. Pip appears to carry her to safety; he succeeds, but is mortally wounded in the attempt. Before dying, Pip orders Seras to drink his blood. (He also gets that kiss.) Alucard has been telling her to do this all through the series, but it's Pip who gets Seras to do it.
Drain someone's blood, and you absorb their memories. Although Pip's mortal body is now dead, his soul lives on within Seras. It was he who asserted control to tear up Zorin. Now that body holds a combination of Seras and Pip - call her Sip - whose full range of powers as a True Undead has only just been scratched.