I'd be happy to classify most R&D as innovation, and much of it is organized. Within most labs, a significant portion of the R&D is for incremental innovation, tweaking existing compounds or products. This is probably the case where innovation is organized. However, it probably represents only about 20% of the innovation potential in any firm.
For some reason, maybe it was the Back to the Future movies, we are led to believe that innovation is done by some slightly off-kilter scientist with bad hair working in a barn off by himself or herself. They tinker with all kinds of technologies and applications with no real apparent goal, other than to subvert a physical law, like travel through time or repeal the law of gravity. This is not a serious view of the potential of the people and the thinking within your organization when it comes to innovation.
A new innovation can be based on a product, or a service, or a process, or a business model. Clearly the guys in R&D have a lock on the technologies and compounds, but rarely have a great understanding of how these new things get to market (that is the processes and business models that provide the means to bring a new product to market). Enron, for all its faults, is really just a company that innovated around a business model - how do we arbitrage and distribute power? They weren't really responsible for generating the power as much as the marketing and distribution, so their's was a business model innovation. In fact they were relatively organized around an innovation in the way electricity was distributed.
Certainly there are a number of other types and capabilities of innovation in your business. The question is, are your people and your processes organized in such a way to recognize a great new idea and bring it to market, whether its a product or a service or a business model? If a great new idea presented itself, how would the teams know? What measurements or metrics would they use to assess the idea? Are they compensated in such a way that encourages them to take the risks necessary to shepard the idea?
If you want an innovative organization, organize your innovations. Provide the teams, the means and the goals to encourage innovation throughout the company. Innovation and great ideas can happen anywhere in the firm, or can be suggested by business partners or customers as well. These ideas can be managed effectively if organized correctly. Outside of R&D, how do you manage your innovations? Do you recognize non-product based innovations?