Beyond Max Frozley
Edit: The name of the thread has been altered
Image linked from batman.ugo.com
Yes, I know it's
a bit unfair to use Arnie's character to illustrate this subject, he's at least generating a bit of conversation on renewable fuels and such.
Anyway, I thought that it'd be worthwhile to point out a few developments that are very much in the pipeline with regard to ICEs but won't find their way into F1 because of the homologation. I'm in no way advocating all these as viable options to the current V8, with or without KERS, but attempting to show that a lot is going to happen in ten years' time. Perhaps enough to render F1 redundant. This is in no way meant to be an exhaustive collection of options available, I just chose a few examples that are innovative but conceptually not very far from traditional engines. I hope this raises discussions, not only on the merits of the engines I've presented (or any that you may want to add), but also more widely on the merits of intellectual freedom, innovation and F1's role in all this.
Wankel to the 3rd power - RKM
http://rkm.schapiro.org/
Image linked from the RKM website
An engine that the inventor (and quite a few backers) promise to be 3-5 times smaller size with equal power output, more efficient, lighter, cleaner, with less components translating into higher dependability and more cost-effective manufacturing.
High hopes compression - to split the Otto
http://www.scuderigroup.com/index.html
Image linked from http://www.treehugger.com
This project comes highly recommended. Among the promises are fuel efficiency improvements of 15% - 30% initially with further improvements possible, potential reduction of NOx emissions of 50% - 80%, lower average operating engine speed reduces engine wear and tear, design flexibility, high torque at low RPM, compatibility with existing engine manufacturing processes and tooling, diesel engines can eliminate half the injectors. I especially envision a F1 team looking into storing and releasing braking energy through this sort of an arrangement.
Another 6Stroke - how many are there?
http://www.sechstaktmotor.de/index.html
Image linked from http://www.sechstaktmotor.de
Promises simplicity, robustness, low maintenance, low production costs and fuel economy.
Going for a spin - Three different toroid piston engines!
http://www.angellabsllc.com/index.html
The MYT (Massive Yet Tiny) engine, promoted by Angel Labs. Promises 20:1 power to weight ratio, only 50 parts make the engine, and it's supposed to be efficient, easy to maintain, clean and small.
Image linked from http://www.stickshiftin.com
http://www.rotoblock.com/index.html
The Rotoblock looks the same, but isn't. Also promises to be dramatically lighter – up to 50% depending upon specific application, significantly increased power to weight ratio, simplicity, no valves and valve train, not being water cooled, adaptability and easy maintenance.
Image linked from Rotoblock website
http://www.roundengine.com/default.htm
The VGT Roundengine is a bit different from the above two. Yet again, torque and power, efficiency, low emissions, adjustable stroke, adjustable compression, multiple fuel capability, modularity, simplicity and longevity are promised.
Image linked from http://www.roundengine.com
Hope these can provide inspiration. I suspect some or all may be familiar to you already. No matter. This is just scratching the surface and frankly there's a lot of more detailed work going on in many fields of study (no need to rethink everything) that is propably more likely to prove to be significant. But I chose these to make a point with regard to the homologation. Sometimes it's more about attitude than realism.
Image linked from http://www.wonderlandblog.com
800hp from a 14" by 14" cylinder 
