Now for tonight's Posting Fury!
The problem with THIS question is that, in general, if I don't LIKE a franchise I don't WATCH it. As I've said about books, life is too short to waste my time on bad books, and the same's true of anime.
About the only good example I can think of is Nihao My Concubine, the second movie of the immense Ranma 1/2 franchise. I thought Ranma was... not too bad for the first few episodes, but after about 10 or 11 it became suddenly clear that there was no longer any intention of moving the characters forward (at least, not until the real ending of the series approached) and the clumsy romance between Ranma and Akane would never be resolved (except, again, possibly at the end of the series, which was a LONG way away); instead we'd have increasingly contrived events to keep them apart while not completely separating them in a way I find Not Funny At All.
Nihao My Concubine manages to distill all of Ranma 1/2 into a single movie and do it well, with several scenes that impressed me then and still work for me well to this day, with a few lines and scenes that resonate well with both Kathleen and myself. So while overall I don't really like the Ranma franchise (or to be honest most of Takahashi-sensei's work), that movie is a lot of fun.
Day 1 - Very first anime:Saint Seiya
Day 2 - Favourite TV series: : The Vision of Escaflowne
Day 3 - Your anime crush: Belldandy, from Ah! Megamisama/Ah/Oh My Goddess! and Shun from Saint Seiya
Day 4 - Favourite Film: Tonari no Totoro/ My Neighbor Totoro
Day 5 - Anime character you feel you are most like (or wish you were): Shikamaru from Naruto Shippuden
Day 6 - Most annoying anime character: Mihoshi, Tenchi Muyo!
Day 7 - Character you’d most like to slap: Sasuke, Naruto Shippuden
Day 8 - Most epic scene ever: End battle of YuuYuu Hakusho: The Poltergeist Report Movie
Day 9 - Saddest anime scene: Belldandy erasing herself from Keiichi's life in Ah! Megamisama/Ah/Oh My Goddess!
Day 10 - Favorite slice of life anime: Koko wa Greenwood
Day 11 - Favorite mech series: Giant Robo: The Day The Earth Stood Still
Day 12 - Best instalment of a franchise you don’t like: Nihao My Concubine
Day 13 - Worst instalment of a franchise you do like.
Day 14 - Current (or most recent) anime wallpaper
Day 15 - A reality check for a genre you like
Day 16 - An anime classic that simply doesn’t work for you.
Day 17 - Best Background Music
Day 18 - Best Five-team (?)
Day 19 - Change you’d like to make to any one anime
Day 20 - Most ambiguous anime character
Day 21 – Favourite OAV Series
Day 22 - Animation studio you'd most like to slap.
Day 23 - Anime you think had the best, or most intriguing art
Day 24 - Favorite anime hero or heroine
Day 25 - Best anime villain
Day 26 - Your favorite harem anime
Day 27 - Favorite anime opening theme song
Day 28 - Favorite anime companion/summoned creature
Day 29 - Best Anime Music Video
Day 30 - Favorite anime ending theme