A whole lot of Hellsing consists of Alucard killing things. This is usually a simple matter of a few blessed bullets, but sometimes our favorite nosferatu needs to tap into something a little stronger.
Let's just run down the list here . . .
The guns. Alucard has two guns. The Casull, which he had at the beginning of the series, is silver; the Jackal, which he got after pestering Walter for a bigger gun (paging Dr. Freud), is black. Both have blessed bullets that leave very large holes in objects and people alike, and will take out most low-level vampires (and whole squadrons of ghouls) in a single shot.
If you want information on the make, model, caliber, and so on . . . I'm the wrong person to ask. Go find a weapons enthusiast. There are plenty in the fandom; Hirano's done his research.
Defying the laws of physics. That's shorthand for "flying, floating, and going through walls." Alucard tends to enter rooms through the ceiling, solely for the shock value. Integral's gotten used to it by now, but it freaked out the Wild Geese when they were introduced.
Messing with heads. And that is shorthand for "inducing illusions or hallucinations, using telepathy, reading minds, and interfering with people's dreams." Alucard prefers to use telepathy to talk to Seras, though she's a bit freaked out about it; and he can read what she thinks in reply.
Shapechanging. Alucard's preferred animal forms are a dog (big, lean, shaggy, black, and eight-eyed) or a swarm of bats. In the opening sequence of the TV series his silhouette is shown turning into snakes, and occasionally there are bugs involved (little white grub-type things). He can also alter his humanoid form; there's the tall, skinny, white-haired version that he had when Integral first found him, and he tends to alter his hair length at whim and sprout extra arms and multi-eyed hellhound heads. And then there's Girlycard. Oh, and, a low-power way to get around? As a mass of blood. (Cheery, eh?)
Absorbing memories. When a vampire drains a person's blood to the point of death, the vampire absorbs the drainee's memory - and soul. Alucard's been doing this for centuries. He does it to the Dandy to get at Millennium's plans; later, he's able to manifest a small army of absorbed souls.
Regeneration. This one's pretty obvious, but basically Alucard can put himself back together when he gets shot up. Theoretically it's possible to kill him, but it hasn't happened yet.
Despite all this, being a vampire comes with its limitations. Sunlight won't kill Alucard, but he can't stand it. Anything holy or blessed is a problem; the bayonets of our favorite Paladin are painful, and something as seemingly innocuous as communion wafers will create a barrier he can't cross if a line is drawn with the crumbs.
Speaking of barriers, Alexander has some of them in paper form; tack them over a doorway and Alucard can't get through that either. Of course, he can't go through any door that leads into a private dwelling unless he's been invited in. One more barrier: bodies of water. He's gotten better at those in recent years, but poor Seras could only cross the ocean in a coffin.
In addition to these limits, which apply to all vampires to some degree, Alucard is held in servitude to the Hellsing family. His more formidable powers are locked up in a control art restriction system and unleashed in measured amounts during limited releases. (Illusion is at level five. Shapechanging's level two.) And only Integral can release the final level - by the time she does that, all hell has already broken loose.