From our 21st Century perspective, we can see Bonnie and Clyde as a traditional film. It's a classic, right? It was shot on film stock, most of it was shot on location in various rural American settings, and many of the interiors were shot in studios. It lacks bells and whistles (although it most certainly does not lack banjo music and gunfire).
And even back in the 1960's there were some pretty straightforward things about this film. The story of Bonnie and Clyde is organized in a very traditional way—it flows in a straightforward, linear fashion. There are no flashbacks, bizarre dream scenes, or disorienting crane shots.
But several elements (such as the nontraditional, chopping editing techniques, and the ironic use of music during the car chases) give it a specific twist.
If you want to look and how Bonnie and Clyde was super-influential, though, mosey on over to Point of View.