-Trigun is something I can't really imagine you not enjoying.
-FLCL follows on the same "I can't imagine you not liking it," note.
-Fullmetal Alchemist: Brotherhood covers beyond what FMA covered, though I feel the second series does a worse job.
-Eureka Seven is a fun shounen anime with fairly interesting characters and story. It starts as a god mecha cliche, but like Evangelion, breaks away from it. There is a small amount of deconstruction of god-mecha genere.
-Claymore is a dark fantasy fighting series. Good action scenes.
-Escaflowne is an older fantasy series that tries to blend shounen and shoujo themes, quite successfully to. Due to the condensed nature of the plot the series has a very epic feel to it.
-Seirei no Moribito tries for a more realism in its fantasy and follows the journeys of a spearwoman and hidden prince. At times the story can be overly emotional, but it is never weak.
-Pumpkin Scissors is just for fun. The plot is meh, but the characters are fun.
-Darker than Black is a somewhat unremarkable series, but not particularly bad. Plenty of fighting in it. Somewhat weak on development.
-Speed Grapher is somewhat similar to Dark than Black, though I feel slightly worse. It does have villains with "WTF" powers as a redeeming aspect.
-Xam'd has some fighting but not very much. I felt the series started with promise but never ended up fulfilling it.
-Samurai 7 is what's on the tin can. For a very cliche story the series does manage to execute it jsut well enough to keep it from being abysmal.
I've actually considered watching Hellsing Ultimate, but I was told that I would have to watch the first series first in order to understand it and that the first series isn't too good. Is that true?
You don't need to watch the first series. Hellsing Ultimate is an OVA more strongly tied to the manga. It covers everything in the first series, just more quickly. 'Sides if you're watching Hellsing for the story, then you're missing the point.
The first series isn't terrible so much as it is slower and breaks away from the manga at the end. You might find it tedious to watch both.