These are anime I feel deserve mentioning, even though they don't really belong in the top tier.
Azumanga Daioh - This is manga in video form. I enjoy it for the same reason I enjoy reading the better parts of the comics every day. Azumanga is light, enjoyable, and occasionally even insightful. It finds the fun parts of everyday life and explores them with characters you can't help but love. It is one anime that I would prefer watching in its original serialized form. Unlike most of my favorites, it is best enjoyed in small, sweet dabs rather than big treacly clumps.
The Melancholy of Haruhi Suzumiya - I feel like this anime fell just short of the mark, not for lack of trying. The episodes are achronological, characters are charicatures that come off as more developed than the conventional characters they parody, the episodes are filled with meta-references. It's really right down my alley but still feels like a guilty pleasure. Unfortunately, some of the scenes, particularly the action scenes, seem to wallow in the cliché the show tries so desperately to transcend. Additionally, although it is initially a cute puzzle, the episode sequencing is eventually just a nuisance. I much prefer watching it in chronological order, in part because the show then ends with one of the best episodes rather than one of the worst. That all said, it's a show I can always watch.
Voices of a Distant Star - This OVA is very nearly a tour de force. The direction is flawless and draws you into a world of raw emotion. Voices fills its 24 minutes without straining its bounds. Unfortunately, there were too many aspects of the framework that just didn't make sense. They kept me from being drawn into the story's emotional dialogue. However, if you can look past the weak parts of the story logic, it is completely enthralling.
Zettai Shounen - If I had seen all of this anime, it'd be in my top five. The first twelve episodes are masterful. It takes a weird premise with odd characters and makes every second of it seem completely real. The characters are flawed but not unreasonably so; they are just normal people in a normal town with weird things happening. The torpid pacing and pastoral atmosphere deftly evokes the experience of being in a rural mountainside town during a lazy summer. Even the dramatic conclusion of the first twelve episodes is handled subtlely. However, I hear the second half of the show is weaker, and I haven't seen it, so I've held off on including it in my rarefied Top Five.
Best of the Rest:
Air - I saw this around the same time I saw Zettai Shounen, and I preferred Air. However, I'm nervous about rewatching it, because I'm afraid it'll seem emotionally manipulative much like Kanon (the elder).
The Big O - My favorite bad anime. I'd never think of defending it, but I always enjoy its balance of Batman zaniness, giant robots, and inscrutable plot twists.
Boogiepop Phantom - Dark and menacing, Boogiepop is frequently difficult to watch. But the horror-mystery is undeniably done with a quality artistic flair.
Cardcaptor Sakura - Pretty good as a children's cartoon goes. It probably falls somewhere below Time Squad and above Courage the Cowardly Dog.
Ghost in the Shell: Stand Alone Complex - Only the first season is worth watching, and it falls apart in the last episode or so. And why can't the Major afford a whole body's worth of clothes? The fan service is embarassing. But the Laughing Man mystery is very well done.
Princess Mononoke - I usually find "message" movies annoying and heavy-handed, but Mononoke is carefully moderate. Its willingness to paint the majority of its characters as somewhat sympathetic is its greatest strength.
Ranma 1/2 - It may be a bit fluffy and repetitive, but it's difficult to dislike a show that refuses to take itself seriously.
Samurai Champloo - Another show where I enjoyed the finale. There are just too many throw-away episodes. Then again, there's ninja baseball.
Trigun - An old favorite. It's not really that great, with the main villian overshadowed by his henchman and inconsistent episode quality. But I still enjoy it for a few great episodes.