I'm assuming I should watch Kenshin TV first then.
Semi-complete list of everything I've seen, with the disclaimer that I probably missed a lot of stuff.
http://myanimelist.net/animelist/Nakor
So after I finished my top 10 I realized I had actually created a top 11 and didn't really want to remove any of them. In the end, I had to make a decision, and trimmed the list to this:
My 10, in no real order:
Slayers Next (and original and Try)
Gunslinger Girl
Black Lagoon
Nanoha A's (and original and StrikerS)
Azumanga Daioh
Excel Saga
Wolf and Spice
Whisper of the Heart
Shura no Toki
Kanon (2006)
Personally, I just can't leave Slayers off the list. Slapstick or no, it's hilarious, it's epic (especially Next), and you hardly have to be an anime fan to like it.
Gunslinger Girl may not make anyone cry, but it's possibly one of the most touching anime out there; it has impeccable quality, amazing characters, and really makes you think. And it doesn't have a second season. NO IT DOESN'T.
Black Lagoon, obvious reasons.
Nanoha A's is in there because, honestly, who doesn't love a great action show once in a while, and A's is the greatest action anime I've seen to date.
Azumanga Daioh similarly is the best the slice of life genre has to offer. Some would argue Lucky Star here, but I loved the Azu characters, plus it's more accessible to folk who've never watched anime before.
Excel Saga may be about as looney as it gets, but it's not the kind of looney you have to be an anime fan to love. Who wouldn't love Excel? As long as she stays on the far side of the screen of course.
Wolf & Spice would be the hardest on the list to introduce to a new watcher, but it doesn't take that long for Horo to grow on you. An excellent character-driven anime with an epic story.
Whisper of the Heart: In my not-so-humble opinion, this work by Miyazaki's studio is better than what Miyazaki himself puts out. It's a slower movie, no real action, not what you'd call an epic, but is a wonderful story - perhaps because, and not in spite, of that.
Shura no Toki is a sort of alternate version of feudal Japanese history. While the focus of the story is the unarmed attack style of Mutsu Enmei-Ryuu, the anime plays this through some important historical events later on. It's well executed, and makes for an excellent story. (In a sense, this might be the 'Kenshin' of my list.)
Kanon (2006) is my replacement for Clannad. The lows were lower, the highs were higher, the art was maybe just a hair better, and even the humour was just a touch better. If Clannad was a masterpiece - and that's what I rated it - then Kanon is a grand masterpiece.
Honourable Mention:
Seirei no Moribito: 11th place on the top 10 list. I'll be honest, I wanted to put Utawarerumono in here somewhere, but it's not really the epic story this was, and the ending totally ruined it.
Clannad: Edged out by Kanon, as above.
Pumpkin Scissors: Great cast, great story, great action, worth anyone's time to watch.