Here we run into the problem that I could be very repetitious here. My favorite OVA/OAV (Original Video Animation/Original Animation Video) series has, for a long time, been a tie between Ah! Megamisama/Ah/Oh My Goddess! and Giant Robo: The Day The Earth Stood Still.
So I think, to be more fair to the larger world of anime, I'll remove them from contention and examine some of the other OVA series I've seen.
OVAs, unlike "direct-to-video" animation here, are NOT anime that you can assume are worse than either movies or real TV series. OVAs tend to split the difference in quality; they have a longer storyline and detail of plot than a standard anime movie, and better animation than the standard anime TV series. A lot of popular anime, such as Tenchi Muyo!, began as OVAs and then became popular enough to be re-done and expanded into other formats. The original Bubblegum Crisis was an OVA series, as was its (much lesser) sequel. One of my strong candidates for "favorite OVA" would be Phantom Quest Corp, an Urban Fantasy with some comedic elements with a hard-drinking, high-spending, karaoke-addicted main character who solved different haunting problems while trying to dodge her creditors. However, it drops points because, well, it got dropped. The continuing storyline and universe-construction stopped because the financiers decided not to continue, so it basically stops dead with no closure. Moldiver, an interesting story concept (boy genius invents a super-powered forcefield generator, plans to use it to be a superhero, his younger sister ends up with it) based in a future world that seems equal parts Speed Racer, Generic Super-advanced Future, and Modern Tokyo, was also a pretty good OVA series marred mostly by what seems to be a rather uncertain direction to the story itself. Record of Lodoss Wars was a fairly long-running OVA series which was an almost picture-perfect D&D adventure translated to animation; this was unfortunately one of its flaws, as you could hear the dice rolling in a somewhat distracting way in the background.
After looking over the ones I've seen and the ones I own, to my surprise I must (aside from my two all time champions) put my chips down for the ... unique swords-and-sorcery OVA series Bastard!! . Based on the manga of the same name, this series features one of the funniest Engrish opening narrations ever, and then segues to what appears to be a fairly standard thud and blunder fantasy adventure.
Anyone of my generation listening starts to recognize some... peculiarities. Such as the countries, and some characters, being named after 1980s heavy metal bands. Which can be quite amusing at times.
The problem the heroes face is that they are up against tremendously high-powered enemies who serve a terribly powerful demon -- enemies so powerful that it's quickly apparent that none of them can oppose it. The only possible opponent to these enemies is, unfortunately, the monstrously powerful evil warrior-wizard Dark Schneider -- who was sealed away by the intervention of a conclave of clerics into the body of a young boy, an innocent boy who has no idea what was done to him. As a man of great passions, the only thing that can unlock Schneider from this ironic prison is the kiss of a chaste young woman.
Naturally, they unleash the dark magician -- who turns out to be at least as powerful as legend, and as soon as he is done saving them, intends to turn around and conquer the kingdom for himself. But he has a weakness he doesn't even know... and, as time goes on, it becomes more and more obvious that his "villainy" was something more complex than the others understood.
He is also one of the most over-the-top definitions of BADASS ever animated. This is the man who RIPS OUT HIS OWN HEART to save a woman he loved. AND THEN RESURRECTS HIMSELF so he can come save everyone else at the last moment.
And he lives up to the title, since he IS the "Bastard!!" of the title.
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. Dragonball GT
Day 14 - Current (or most recent) anime wallpaper: Picture of Son Goku with Shen-Long done by my wife Kathleen
Day 15 - A reality check for a genre you like : Power-warrior anime and internal sanity/consistency!
Day 16 - An anime classic that simply doesn’t work for you: Neon Genesis Evanjellydonut... er, Televangelist...er, Evangelion
Day 17 - Best Background Music: Giant Robo: The Day The Earth Stood Still
Day 18 - Best Five-team: Yoroiden Samurai Troopers/Ronin Warriors (no link, too expensive)
Day 19 - Change you’d like to make to any one anime: Specific Change: Eliminate one nasty action from the history of Juraia-sama in Naruto/Naruto Shippuden. General Change: Eliminate the Saiyajin focus and expand capabilities and screen time for all major characters in Dragonball Z.
Day 20 - Most ambiguous anime character: Selected Maraich and Patalliro, from Patalliro!
Day 21 – Favourite OAV Series : Except for two I've already mentioned, Bastard!!
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