There's a sub-genre of shoujo called "
Mahou Shoujo", or "magical girl" shows, of which Card Captor Sakura is one. If you like CCS, then chances are you'll find many of the more famous ones in this genre appealing as well. Examples: Sailor Moon and Magical Girl Lyrical Nanoha. Despite what others may say, there is seriously no shame in liking this stuff. Some of it is seriously awesome.
Haruhi is different in that it's really a genre buster series. It's technically shounen, I guess, but damned if it isn't all over the map.
Cowboy Bebop is an excellent one I recommend you check out, and as an added bonus, I would actually recommend watching the
English dub on this one. This show is the exception to the rule that the original Japanese is better. I found the English dub superb. This one is another one that kind of has no genre. If I had to categorize it, I'd say "Jazz Western with an IV steadily dripping awesome into its veins." It's excellent.
If you're into classic Giant Mech animes, I can't really help you there. I'm pretty unfamiliar with it. However, I've always heard good things about the Gundam series, even though there's about sixty different ones.
If you like deconstructions of genres (that is, if you like watching someone take a genre and proceed to twist the "rules" of that genre into a dark tale or showing what would happen in a more realistic situation), then there are a few different series to check out.
Neon Genesis Evangelion is a classic, and is required reading for almost any anime fan. It's a deconstruction of the Giant Mech genre that was wildly successful and influential on the genre on the whole. Before NGE, the genre was fairly lighthearted. Serious, but the hero would usually win, villian got his comeuppance, etc. After NGE? Holysh*t the whole genre went grimdark.
At least, this is what I've been able to gather. This was all a little before my time. It's also one of the trippiest animes you will watch, especially towards the end when the studio ran out of money. Has a movie to watch afterwards, and is currently doing a remake of the series in the form of 4 movies.
Puella Magi Madoka Magica (Madoka for short) is a deconstruction of the Mahou Shoujo genre. It's been described as NGE with magical girls. It's a lot more recent, and deconstructs the genre pretty well, going grimdark
fast.
For more lighthearted, really good animes, check out
FLCL, pronounced in English as "fooly-cooly" (it's short, only 6 awesome episodes), and
Tengen Toppa Gurren Lagann.
Death Note is an excellent one to watch if you are in to intellectual thrillers/mysteries. It's about a guy who finds a notebook that kills whomever's name is written in it. Told from the killer's point of view.
If I had to pick one anime from this list I feel is most required to watch, it's FLCL. No doubt.
Edited, Feb 12th 2012 8:51pm by IDrownFish