Killjoy, I came into this thread expecting some sort of chatter about how another person has converted to furryism, but I find talk about one of the greatest anime of all time.
And yeah, the anime gets better as it progresses, you won't regret watching it. Heck, I bet you'd even shed a manly tear or two after you're done with the series.
Maybe you should check out my anime list in my sig (yes shameless advertising) to check for some random anime to watch if you really have no clue on what to watch next.
I'd recommend Clannad (both seasons) if you haven't watched them. The anime is really amazing, with really hilarious scenes and really sad scenes, so you'd definitely cry, both tears of laughter and sadness. The first season might not really cause you to feel much, but the second season is touching beyond words.
Not forgetting Mahou Shoujo Madoka Magica (or whatever it's called). It's one of the more decent anime of its season, and considering the fact that it has only 12 episodes, it wraps itself up rather nicely, and at the very least you'll feel something after you're done with it.
And don't let the "Mahou Shoujo" name fool you into thinking that it's just some typical magical cheerful slice of life yapyapyap blahblah boring anime, it has a pretty dark story, so it's definitely worth a watch.
Durarara!! is also rather decent, no idea why I brought it up now, but it's worth a watch if you're bored.
I'd also recommend Hayate no Gotoku (both seasons). It doesn't really have a main plot, but hell, it's one helluva funny anime. You'll laugh at the scenes in the anime so often that you won't even care about it not having a main plot. The second season focuses slightly more on Hinagiku romance though. But still.
Eureka Seven is also a good anime to watch. It has like, 50 episodes, and the story starts out rather slow at first. But this is one of those series that you'll have to watch to the end to fully enjoy, if you drop out halfway then you'll probably find it some generic mediocre mecha anime. Watch it to the end and you won't be disappointed, I assure you. The characters are rather well developed, so it's definitely worth it.
Sayonara Zetsubou Sensei is great as well. It's a rather weird anime (typical Shaft anime), but like some of Shaft's other anime (Bakemonogatari, Mahou Shoujo Madoka Magica), it's amazing in its own way. The comedy is pretty damn funny, and there are tons of anime references (including Gurren Lagann) but you'll have to watch out for them (observe the classroom chalkboard especially closely). It's worth the watch, and it has an awesome opening theme song as well (BURE BURE BURE BURE). There are 3 seasons, I'm only done with the first though. Also, lol wall of text.