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 Harem Series where a loser meets several women who immediately fall in love with this loser for no clear reason.
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.
Getter Robo was the first Combining Mecha and Raideen -almost- was the first Transforming Mecha. Both concepts have been imitated, subverted, ripped off, deconstructed and reconstructed countless times since the seventies by countless mecha shows.
An interesting subversion of this comes from King of Braves GaoGaiGar. While a lot of Super Robot series following Evangelion tried to copy its style, whether it be in character drama or enemy designs, GaoGaiGar was almost a violent throwback to the genre's roots drawing much from Getter Robo, Mazinger Z, Kotetsu Jeeg and the like, it has since left its mark on the genre, helping to keep the popularity of the Hot Blooded hero type that such series became famous for.
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.
The success of The Animatrix paved the way for direct-to-video anime anthologies of popular Western franchises, animated by different well-known studios. So far, Batman got in the act with Batman Gotham Knight and Halo with Halo Legends. Dead Space and Dragon Age has also followed suit.
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 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.
Yuri Genre series in recent years have taken a lot of inspiration for Maria Sama Ga Miteru. To specify a lot of them have lots of blushing, are set in an all-girls school (often Catholic), feature a Sempai Kohai dynamic, and are rather like the Romantic Two-Girl Friendship trope. There have been a fair share of parodies though, such as Maria†Holic.
