Although some people like Arucard x Seras, Arucard x Integra makes much more sense to me. Arucard x Seras is virtually non-existent in the anime series (except perhaps for the first episode), but there are plenty of hints of ArucardxIntegra. AxI is particularly obvious in the later episodes.

Arucard and Seras have a teacher/student or father/daughter relationship. Seras has a hard time adjusting to her new nature; however, she tries to resist these darker urges (such as her desire to drink blood) and desperately wants to cling to her human side, even though she is now undead. Seras sees Arucard as being similar to her in that they are both vampires, ones that are different from the Freaks; not only that, Arucard is the one who 'gave birth' to her. Therefore, Seras naturally looks up to him and seeks guidance from him. Possibly, she may even love him, but this love is non-romantic; instead, it is derived from her admiration for him. Arucard recognizes Seras' need for direction and tries to provide some; however, she continues to hold onto her humanity, and this draws his annoyance and contempt. As suggested in episode 11 (and at other points), Seras may also regret becoming a vampire. Whether this is true or not, though, is somewhat irrelevant: the fact remains that until she can cast off her human ideas and emotions, she will always remain on an unequal, subservient position to Arucard. He will never view her as anything more than his 'servant' (or even less) until she, by her own free will, becomes a true vampire.

As stated in the Relationships section, Arucard has feelings for Integra that go beyond the simple 'Integra == human, human == bad, Integra == master, master == bad' mindset. At the very least, he has some fondness for her, and there is obviously an emotional tie to her. As for Integra, she, too, has feelings for Arucard. Their relationship, though, is complicated, and they definitely have a lot of unresolved tension.

Although the anime seems to support AxI, a romantic relationship between them would be difficult - not impossible, just far from easy. Their obligations and their relationship as human master and servant vampire are rather large issues. Integra doesn't hate Arucard, but she does hate the undead, and maintaining a relationship with a vampire, especially one she frequently conflicts with, is bound to have at least a few kinks.

Even starting the relationship would be hard, and it's unlikely that Integra would be the initiator. For despite Integra's cold, focused personality, she is still a fairly inexperienced young woman. She probably has had few romantic relationships, and most of her other relationships are professional and emotionally distant. Furthermore, her pride and sense of duty would get in the way. Even if she wanted Arucard, she would deny those feelings for him; she could not act upon her desires, would not even admit them because she is completely devoted to the responsibilities of her birth - blood, country, religion. In short, her inability to become involved with Arucard would be driven by the same thoughts and ideas that prevent her from mixing their blood for strength.

One complication that is quite interesting (which has been brought up in Japanese fanfics) is the likely necessity of Integra to eventually marry and have an heir. Her devotion to Hellsing and its continued legacy would lead her to fulfill this obligation, even though there is no indication that she ever wants to marry; it's also difficult to believe that she'd easily submit to any man as a mere 'wife.' However, the future of the Hellsing family would be enough for Integra to marry, even if she were against the idea. Given Hellsing's future versus having Arucard, she would probably choose Hellsing.

Deciphering Arucard's feelings is harder given that we don't truly understand the nature of his contract with Integra; specifically, should Integra die, his fate is unclear. If his life is tied to hers (which is actually unlikely), then he should be selfishly motivated to keep her alive. While this theory would seem to explain many of his actions, it does not explain away his genuine fondness for Integra. On the other hand, if Arucard is freed upon the death of the last Hellsing (more likely), then much of what he does for, or with regard to, Integra is driven by their emotional bond.

Arucard, though, obviously has less reason to be restricted by feelings for Integra. He's not human and doesn't care for human ways, and so it's much easier to see him initiating something between them.

There are many reasons why Arucard and Integra would be a good pairing. Given the length of time they've known each other - ten years, during which Integra grew from a child into a woman - and the complexity of their relationship, it's hard not to wonder how far their feelings for each other really go. They also match up very well; they both have very strong and demanding personalities, and these are qualities that they both recognize in the other. Plus, they're just damn hot together.