Mister Satan from Dragon Ball Z has fought against Cell and Buu, but he never died. Actually, he is one of two characters (the other is Uranai Baba) who never died in this series (excluding the people who were born after Kid Buu's death).
Openly acknowledged as being the main (and besides cooking, perhaps only) ability of Milfeulle in Galaxy Angel, perhaps related to her usually selfless behaviour. (See also: All-Loving Hero) This ability is so powerful that, on the day her normally good luck reverses, a black hole almost swallows the entire galaxy. She is also The Ditz.
Matsuri gets promoted from Dojikko to The Fool in the second Ichigo MashimaroOVA, in which she is pressured into shooting Miu with a rubber band which knocks Miu across the room, and then accidentally blocks Miu's kick in such a way as to send Miu writhing in pain on the ground.
In You're Under Arrest!, the sweet tattletale Yoriko Nikaido was actually the higher-ranking graduate from the police academy... through several strokes of luck (in the shooting range she aced by shooting in with her eyes closed, in the martial arts stage she slipped and this let her pin her rival to the tatami mat, etc.), much to the fury of her friendly rival, Rich Bitch Chie Sagamioono.
Megumi Minami, Kintarou Tooyama, and especially Kyuu Renjou from Tantei Gakuen Q.
Judai (Jaden) Yuki in Yu-Gi-Oh! GX. Saiou (Sartorius) even designates him to the tarot card. However, in the third season, this is Deconstructed as his back story is revealed.
It is possible that season four's events insinuate that Saiou himself is The Fool (in an inverse connotation, Tarot-wise), allowing himself to have been manipulated by fate and demonstrating no control over the outcome of events he put into motion.
Isaac and Miria from Baccano!. So much that the benefits of it seem to be contagious. For example: accidentally stealing the Elixir of Life and then, mistaking it for booze, cheerfully sharing it with twenty-odd affablemafiosos that they've just met.
In Gintama, Sakamoto Tatsuma pretty much epitomizes this trope. He appears clueless most of the time and reacts to everything with a cheerful disposition and his trademark laughter. Though this may be a case of Obfuscating Stupidity, as he is also a successful businessman who owns a fleet of armed merchant spaceships, and in a flashback is shown to have been a serious, intelligent resistance fighter who gave up fighting for a lost cause and turned to commerce when he saw that the latter would be a more successful and less bloody way of bringing about better relations between the inhabitants of Japan and the Amanto aliens.
Sailor Moon has the eponymous Moon/Usagi, who found out she was Sailor Moon after rescuing a cat (Luna) from a bunch of bullies, and survived her first battles out of sheer luck and the support of her Mysterious Protector. Character Development improves her as the series continues and she matures as a person and fighter, however, she never would have survived the first season if it wasn't for her fool's luck.
Femio from Princess Tutu is almost an over-the-top parody of the trope. When the Dark Magical Girl, Princess Kraehe, casts a spell on him so he'll literally and figuratively give his heart to her (so she can feed it to her father), he almost falls for it...until he declares he can't, because his narcissism makes him believe he should be available for all women to love him. Both Kraehe and the eponymous Magical Girl are left speechless by it.
Monkey D. Luffy of One Piece has drifted to this now and again. In the second chapter, he gets pulled into a giant whirlpool and survives because he hid in a barrel. In Skypiea, he gets trapped into the belly of a giant snake and avoids detection from Eneru's ESP. And in Impel Down, he falls from Level 3 Starvation Hell to Level 4 Inferno Hell by...falling into the Hell's giant, burning cauldron. However, in doing so, he managed to bypass the normal entrance, where the prison's entire staff was waiting for him, including the nigh-unstoppable Warden Magellan. Luffy tends to avoid danger by bungling towards slightly lesser-danger.