I was not exactly enamored with Hellsing after I watched it the first time. However, due to its widespread popularity I decided it warranted a second viewing. (This isn't really much of a feat as it's only 13 episodes long.) However, even after seeing it twice I'm still not particularly impressed. There are certainly things I like about it, but probably an equal number of things I don't. I'll try to articulate these points without revealing too many spoilers.
One preliminary note: The proper English spellings and pronunciations for the Hellsing characters' names have been hotly debated. I am unconcerned with what the "official" names and spelling are supposed to be and I don't care what the fansubbers say. I shall refer to the main protagonists with the following names: Alucard, because (1) it's Dracula spelled backward and (2) Arucard just doesn't make any sense, although to be quite honest, it actually sounds as if everyone is saying Arkard. And Celes Victoria instead of Ceras or "Miss Enormous Anime Rack," and Integra Wingates Hellsing (pronounced IN-teh-grah—not like the car) instead of Integral, just because that's what they sound like to me. (These two could really go either way.)
From a stylistic persective, Hellsing is an interesting take on traditional vampire lore. Most of the usual mythology is acknowledged, but there are many notable variations (e.g. sunlight aversion). Unfortunately, the most significant departure and main focus of this first (and likely last) season, the creation and proliferation of artifically induced "freak" vampires, is not especially compelling.
Much of Hellsing's appeal is actually found in its little details. I find the crudely animated previews for the coming episodes thoroughly amusing. I also like the way Celes pronounces "Mah-stah." And I like that although the show is generally dark and desaturated nearly all of Celes' scenes are richly highlighted with her blue/red eyes and bright uniform.
From this pronounced use of color, one could understandably assume that Celes Victoria is the main focus of the show. Indeed, Hellsing does nearly begin this way. The early episodes dealt more with Celes learning what it meant to be a vampire. I would have enjoyed Hellsing much more had they pursued this theme to a greater extent. I was intrigued by the fact that Celes only changed physically when she became a vampire. Since she retained her personality and character traits after her transformation, she had to deal with the weight of immortality's loneliness and her own aversion to her growing thirst for blood. Regretably, the show instead centered around the unremarkable freak vampire storyline and base attempts to generate eminently predictable Alucard fanboy worship. The focus on Alucard is one larger shortcomings of Hellsing. Nearly all of the other characters are more interesting—the protagonists are, anyway.
The biggest problem with Hellsing is its fantastically uninteresting villains (with the notable exception of Alexander, who arguably is not really a villain). They're boring and insipid and forgettable. Furthermore, their fight scenes are tedious exercises in one-upmanship—increasingly absurd without being at least visually captivating.
Another problem is the surprisingly uneven animation. Sometimes Hellsing looks great. Sometimes it just looks terrible. It's as if each episode was generated in a collaboration between professionals and rank amateurs.
Overall, I think Hellsing would have been much better had it focused on Celes Victoria's self-discovery and growth as she learned what it means to be a vampire and dealt with her fate. This was the path the show started with before it decided to dedicate all its time trying to convince its viewers that Alucard was cool. Uh, no, and his fashion sense is deplorable.