I grew up back when it was simply Japanese cartoons on the old UHF dial. They have influenced Western pop culture more than people realize. If you've seen The Lion King, you know Disney only steals from the best. ;)
It's been speculated over the years Lucas was influenced by Space Battleship Yamato, which was airing around the time George visited Japan. The English dub, (retitled Star Blazers) hit American airwaves in 1978, no doubt as a result of Star Wars' success.
Star Wars characters often turn up in anime as an inside joke. I definitely saw Vader in the dance club scenes of the Lensman movie.
There's also this bit of amazing animation from 1983...