I don't know which company has been most innovative, because I don't follow the entire knife industry that closely. So, I'll just say the most innovative company I know, instead of the most innovative company of all.
Busse.
A lot of their innovation goes unnoticed, because it is more subtle than a new mechanism. Also, a lot of their innovations become such standards in the industry that they come to superficially appear similar to other knifemaker's wares. But they are constantly experimenting, and pushing new limits.
They're just about the only company out there that has designed their own steel from scratch, INFI, reputedly involoving a new steelmaking process, as well as containing an element not previously used in the cutlery industry. Now they have made a new steel for their new Swamp Rat line of knives, SR101, a variation of 52-100, which allows them to achieve very high steel performance for a rather moderate price. They also have their own ("transverse wave") method of heat-treating their knives to maximize the steel's performance. Because of these innovations, they have been able to create high performance steels that many consider to be the best in the cutlery industry.
Getting beyond their steel, their other materials are also innovative, such as the Resiprene C handles on their new line of knives, and their long-wearing crinkle coatings.
They are also innovative in the area of design. Some of their blade designs, like the Paul's Hatchet, are quite different. They have created their own type of serrations, which are sturdy enough for chopping, easier to sharpen, and still cut and tear well. Then there's the Ergo handle design. And the BAT tip design, to get the best combination of penetration and tip strength. And the experiments to create the grippiest ground-in pattern for micarta handles. And the assymetrical edge (1/2 convex and half flat ground), for combining strength and ease of sharpening.
Busse Combat Knife Company is now readying to release their first folder, reputedly with a new type of lock.
Busse Knives constantly evolves their line, often with true innovation.