Osu!
As the lot of you have already pointed out, Ashihara concentrates on kumite, and to move around the opponent, out of the impact zone, and into a better position. We also allow grabbing and throws. We don't have any traditional kata's, but kata's that has the same basic system, with different themes, such as Kumite, Nage etc.
I'm somewhat shocked to find out I'm on the internet, though. Meaning I'm on the video from Nęstved, Denmark (the Ashihara vs. Kyokushin one) It's a movie with fighters from my dojo. Also, the one with the Sabaki rules, wherein some of my friends is in. :S They didn't know that it existed on the web either, hehe.
Here is a movie clip from last saturday, at a tournament called 'Russia vs. the World', where the best Russian fights against the best non-russian in diffferent styles.
http://youtube.com/watch?v=BIS7JC1Uuak
If you want, I can post some more Ashihara clips.
[EDIT: This is a movies from the Sabaki Challenge Spirit '97, the annual World Cup tournament held in Viborg, Denmark. Enjoy.
http://www.ashihara.dk/media/146/video/SCS97action.mpg ]