This series is amazing, as to be expected from anything written by Chiaki J. Konaka. Vampire stories have been perverted and sucked dry...bad pun. For once there is a modern nosteramous, where the undead are something to be feared while providing interest to the viewer.
It is important to compare this anime to the manga and OVAs. The better bits to their story includes a more intriguing opening, the nature of vampires is better explained, Seres has a darker side to her, and they are better paced. On the other hand, the TV series has a far more belivable narrative, the conflicts are better, it sticks with the dark atmosphere (where the OVA attempts to be too comical), and it does not become an outragous war against nazi vampires. Overall Hellsing is much better than Hellsing Ultimate. While not perfect, its flaws are minor, the biggest being the fact it runs only 13 episodes.
The story of Hellsing is fresh and full of soul. Equally it is dark, but appropriately so, allowing for subtle comic relief. Unfortunently it is rushed, and at the end the viewer finds themselves feeling robbed of another 13 episodes which could have been easily fit in. An example, after the first episode Seres is immeadiatly put into action. This would have been a good place to insert a show where she (and the viewer), learn about what it means to be a vampire. The same could have been done with most everything, including leading to the finally. Other than this there is little to complain about.
The art and animation is done in an interesting style, not as exceptional as in the OVAs which were on par with ghost in the shell, but relatively fluid and beautifully drawn.
In terms of sound, this is a rare example were the english dubbed is better. Probably this is due to the setting taking place in London, therefore the british accent is more fitting. The effects are some of the best, especially considering the firearms. As someone who occational shoots recreationally, some scenes brought forth the smell of smokeless powder and feeling of stiff recoil, which is uncommon.
Character development focuses mostly on Seres. The series could have done with including her darker side, which would have added to the already excellent theme of losing humanity to monstosity. As mention also needed twice the time to properly grow, 13 episodes is far to little time. Supporting characters are all excellent, little is to be said. There are other anime with better characters, but they hold only a slight edge over Hellsing.
In total, it is easy to greatly enjoy the Hellsing anime. Many would find it among their favorites. Its flaws are mainly in how short it runs. At this moment one may only hope that someday a second season may be made.