At least four recent films play off this narrative concept
A great deal of Pulp Fiction dances in and out of three different stories while giving you different versions of the same period of time.
In The Usual Suspects the story starts near the end, goes to the beginning and then gives you the end after the end. You are also shown the story through the eyes of a least two different characters, so that borrows from Rashomon as well.
Although I have not seen it, several people have let me know that Magnolia has a similar concept-telling/showing a single story through the eyes of different characters. (thanks panamaus et. al).
The best and hippest version of Rashomon is Go!, a hyperkinetic party/road trip movie that is set against a Rashomon template. Each of the three stories is carried through from beginning to "end" from the point of view of three different characters. No one version is the "right one." Although the characters interact to some degree, each story is seperate and distinct.
My advice : rent Go!, then try and find Rashomon on tape.