The manga and the anime are different story-wise and character-wise. For example the main characters in the manga are Integral Hellsing and Alucard, leaving Seras Victoria in the background, while the anime revolvs around Seras Victoria and her point of view about vampirism. Also Father Alexander Anderson has deeper personality in the manga than just a mindless killer as depicted in the anime.
Story-wise episodes 1, 2, 3 (the meeting with Father Anderson), 5&6 (the attack of the Hellsing HQ), and 10 (the flashback of how Alucard and Integral met) are close to the manga and the rest of the plot in the anime is totaly different.
"What a perfect night. It's the kind of night that makes me want to get a bite to drink." -Alucard
Alucard is under the control of her master, Integra Wingates Hellsing, who is the leader of the Hellsing Organization, a group of undead hunters who's goal is to cease all earthy activities of those not of the undead classification. Now, there are also secondary characters like Walter, the Hellsing family's butler, and Paladin Alexander Anderson (in Japanese it's Paladin Alexander Andersong), as well as the Nazi organizations that seem to appear quite frequently in this.
There are variants of Hellsing, which include OVAs (original video animations) and the anime, which is thirteen episodes long.
It is disputed which ones are better, because many fans prefer the manga over the anime. The OVA is the anime-form of the manga exactly, but the anime is not anything like the manga at all.
Then were are things like "Hellsing: The Dawn" which feature much younger versions of Alucard and Walter as they fight the Nazis. That's when Walter is nicknamed "The Angel of Death" by Alucard. It is a highly recommended anime by those who like horror and such, but in reality, it's more of a thriller than a horror. There is a lot of swearing as well, as well as blood and death, so it is not recommended for children under the age of thirteen.
To learn more, actually reading the manga or watching the anime is also recommended.
Thoroughly recommended, especially for fans of vampires or action anime. Not for younger viewers.
Guy 1- Dude, have you watched Hellsing?!
Guy 2- No, I've read the manga. Isn't the whole Nazi thing cool?
Guy 1- What nazi thing?