Series' I liked, and why:
Hellsing: A secret paramilitary organisation that has battled vampires for centuries, has to contend against a wave of artificially created undead, with the aid of Alucard (think about it), an ancient and fearsomely powerful true vampire. It's slick, and very cartoony-violent, and also has something of a gun fetish, but it's fun at the same time, with an interesting unfolding plot and memorably weird characters. Only strike against it is the low ratio of episodes per DVD disc.
Excel Saga: You might want to watch some other anime before this as it is first and foremost, a merciless piss-take of other genres. The plot, such as it is, revolves around a hyperactive teenage girl (Excel), who works for an organisation called ACROSS, with vague goals of overthrowing corrupt modern government, but that's really just a framing device for parodies of other genres, including horror, survival alien invasion, and sports drama. I found the first episode confusing and not especially funny, but everything after that is pure gold.
I've seen some of Berserk, and really liked it (it has some great battle scenes), but be warned that the ending, which I've not seen, pisses quite a lot of other fans off.
Second for Trigun. It's a mix of sci-fi and Western, focusing around a mysterious wandering gunman who's acquired a reputation as a walking disaster area and death incarnate when he's actually a nice guy, and a pacifist to boot. It's good for the start, though the goofiness might be a bit offputting, it's worth sticking with--a few episodes in, the tone becomes a little more serious, the sci-fi elements are expanded on, and we start finding out about the backstory, and I found it incredible.
Evangelion really is a love it or hate it show--it has a massively intricate backstory, and you have to do a lot of conjecture to put it together. There are also two endings, both of which are loved and hated in equal measure. Some great giant robot battles though.
Read or Die: Supposedly a series, but more like a feature film broken up into three parts, this is about a nerdy, mild-mannered librarian, who happens to have incredible paper-related powers, who works with her partner (who can become intangible) for a international librarians task force, to combat cloned historical geniuses with incredible steampunk technology, called the I-Jin. It's as quirky as it sounds, but it I found it wonderful. Also, for the price-conscious you only need to buy one DVD.