The surprise success of the manga Love Hina, a story about a loser who through hard work, learns martial arts, becomes successful, slowly wins the women in his life, and finally gets to marry his first love. This gave rise to a ton of low-quality Harem Series where a loser meets several women who immediately fall in love with this loser for no clear reason.
Originally, Double Team in the anime used the rapid afterimage trick, after Naruto became popular, now it works like Shadow Clone Jutsu.
Well, it is called "Kage Bunshin" (Shadow Clone) in Japan.
Super Robot Genre shows like Tetsujin 28 already had their own success, but it was Mazinger Z that solidified the concept of piloting a robot (via a cockpit within its head, rather than remote control) and started a revolutionary trend that attracted toy makers and captivated children. Such influence would eventually lead to all sorts of landmark works that keep the said genre alive and relevant to this day. Pretty much everyHumongous Mecha show created after 1972 owes something to Mazinger Z, either because they copied the tropes established by this series or because they tried averting them, subverting them or deconstructing them.
Anime was largely an underground movement in the States before the success of Power Rangers, which led companies to look for more Japanese material to localize in 1995, including Ronin Warriors, Sailor Moon, Eagle Riders, Teknoman, and Dragon Ball. The Pokémon phenomenon several years later advanced it further, resulting in the localization of not just more Mons-flavored shows, but also the shonen genre in general. American TV producers have tried to cash in on this as well, but, not wanting to pay for an existing series, create their own. For proof that this rarely ever works out, look no further than Dragon Booster.
Revolutionary Girl Utena now has at least one imitator, Shitsurakuen. It's about a tomboyish young girl who gets accepted to an exclusive private school and wears shorts instead of a skirt with her uniform (although they came with the uniform, to her confusion). She sees herself as a knight defending the oppressed girls of the school, who are used as weapons/objects by the boys, especially the head of the student council. There is much Ho Yay and Les Yay to be had, too. At least here there's a sci-fi reason for the weapons coming out of the girls' chests: the whole campus is a 3-D stage for a video game.
Dragon Ball's impact on Shonen manga is, well... impressive — to say the very least, its influence now impossible to not see in almost any work in the subgenre. Although not the first employ the vast number of the tropes its most associated with, it became the de facto face of them. To this day, Shonen, and various Anime in general that use elements from, pay homage, or parody, this series and continue its legacy. For proof, one need only look as far as these three anime — often considered the most current and direct of its spiritual successors: Naruto, One Piece, and Bleach.
Dr Slump has a follower of sorts in "Cybot Robotchi" AKA "Robby The Rascal". Both feature a horny, awkward Bungling Inventor with a Punny Name living in a small town in the middle of nowhere populated by weird people and animals, who creates a robot with huge powers but the mindset of a kid (and a lot of other silly and bizarre inventions). Hilarity Ensues, etc.
Neptunia was a video gamenote it later received a short manga and an anime is in production that centered around Console WarsAS A VIDEO GAME!, with large amounts of Fanservice. A manga/anime series entitled Aoi Sekai no Chuusin De was created which has a similar premise, but with several differences. There's significantly less Moe, the characters are based on video game characters/franchises themselves instead of companies, and the console war is more specific, focusing on Sega vs. Nintendo.
Kimi ni Todoke inspired lots of Shoujo Genre manga (of varying quality) with a shy girl as the lead. Unfortunately, some mangaka took it too far and made them weak, spineless crybabies.