In a story about an organization that hunts vampires, here's the fundamental twist: the Hellsing organization has one working for it.
He's suave, he's strong, he's generally considered to be sensationally sexy, he has swarms of fangirls, he sports a dashing set of fangs . . . and the vampire Alucard is a servant of the Hellsing family, and the organization's trump card.
Alucard's reaction to this state of affairs depends on whether you're watching the TV series or reading the manga. Watching, you'll see him hissing that it's pathetic for a vampire to serve humans (although he usually says this to other vampires, right before shooting them). Reading, you'll see him rather enjoying himself, and using his position to taunt Integral.
Watching, you get his contempt for humans; reading, you get his contempt for monsters. Either way, he relegates most beings - human and vampire - into a category better described as "dogs": not worth the bullet you shoot them with.
His master, Sir Integral, is one of the people he respects. She found him in a cell of the Hellsing mansion basement at age thirteen and refused to be intimidated by him; when she didn't back down, he bowed to her. Since then, although he can't physically harm her, they've engaged in regular verbal sparring matches, during which a sardonic smirk never leaves his face. Alucard likes to bother Integral; the fact that she can return in kind is what he likes about her.
Besides, he thinks she's hot. (But who doesn't.)
The Hellsing family's retainer, Walter, is another of those rare individuals that you could call him close to. The vampire seems regretful about Walter's aging, and the two have thoughtful conversations. Theirs is a connection forged through fighting together on the battlefields of World War II. Of course, back then Alucard had the form of a very girly teenager.
When you're 567, I suppose you want to try everything once.
At first glance, it wouldn't seem like Alucard respects his fledgeling vampire Seras. He orders her around without much explanation, and is prone to scaring her. He doesn't understand why Seras tries so hard to hold on to her humanity; but Alucard sees the potential in her, and is pushing her to bring it out. ("What does not kill you makes you stronger.") He's a warped sort of father figure, and he is in fact prepared to be proud of his daughter.
Alucard's searching for a worthy opponent, but so far the best he's found is the Iscariot organization's counterpart trump card, Paladin Alexander Anderson. In the TV series, Alucard's hoping for a vampiric opponent; in the manga, he knows it has to be a human, not a monster. He recognizes that Alexander is brave, and hopes he can become as strong a rival as Van Helsing was. In the meantime, the vampire shamelessly mocks the priest. ("What are you going to do? Chew me to death?")
Yeah, Alucard is Dracula. If you didn't catch that already.
So there you have Alucard. Aloof and mocking on the surface. Very complex underneath. Oh, and he has guns. Big guns. He may be an enigma, but there's one aspect of him that's very simple: he aims, he fires, and things go boom.