Eva's often brought up as one of the most influencial animes of all time. It has never really made that much sense to me. At its core, Eva is the pure definition of cliche. Its one of the most commonly used genre in anime, the 'teenage pilots a powerful robot' type. Nearly every so called 'Eva clone' out there isn't really an Eva clone, just another member of this same group of shows.
There is one big impact Eva's had though. You see, as Eva reached the peak of the series, not only did the quality of the show vastly increase, but the content got much worse as well. In episode 16 we see Unit 01 tearing itself out of an angel. In episode 18 we see Unit 03 strangled, get its head crushed, its limbs torn off, etc... ending with the entry plug that contains Touji cut. In episode 19 we have decapitations and dismemberments, not to mention an Angel getting eaten. Episode 20 has an offscreen sex scene between Misato and Kaji. When these scenes aired in Japan, the public was shocked. After all, Gainax didn't exactly get all these scenes fully approved by the network.
Anno and co. created a huge problem with what they had done. The climate became a much tougher one, and things such as the Eva series battle, which was originally supposed to be part of the series' ending, was axed. Amazingly enough, Eva had an effect on its own ending, which resulted in the craporama we got in episode 25 and 26. If they hadn't gone so overboard in episodes 16-20, the original ending may have been aired.
Eva's impact lasted long after it went off the air. The most well known example is a show thats just as popular, if not more popular than Eva, Cowboy Bebop. Cowboy Bebop aired in Japan in 1998, roughly 2 years after Eva. But unlike Eva, Bebop didn't even get to air half the series. Due to the tough censorship climate created thanks to Evangelion, 14 of the 26 Bebop episodes were not aired. The most noticable example is the first episode, the fifth episode, which is the start of a story arc that goes throughout the whole series, and the final 8 episodes of the series. Thats right, Bebop didn't even get to air its ending on TV. You can thank Gainax for that one.
So when you talk about Eva's impact on the medium, yes, you can say it had a big one. But I wouldn't be too proud of it. Eva's impact was very detrimental to other shows, especially Cowboy Bebop. Eva's impact on the medium is not something I as an Eva fan would be willing to gloat about.