For GA.. I think diesel powerplants will become more and more popular. No lead keeps the EPA happy, the fuel is common everywhere, is not a niche market like 100ll and can made from plants and leftover fry oil. Even Continental has a certified diesel now. Electric powerplants may have a future too, if they can develop much, much better battery technology. I remember reading about a prototype electric 172, I think the total run time on a full charge was like 30 minutes... and that was with solar panels all over the top of the wing helping it. Also I bet we will see more and more stronger, lighter composites in airframes. Cheaper small turbines (think Allison 250) for small singles would be great too.
For airlines... Personally I hope that ultra-high bypass and unducted fan (propfan) engines make a comeback,
remember this guy...
Back in the 80s after the oil embargo they where all the buzz and where gonna be the future because of their superior efficiency, but that all faded out when fuel got cheap in the 90s. Now that fuel prices are high again I keep thinking they will try and develop them some more. The biggest issue as I understand it is that they are just to dang loud. Also I bet after the 787 all new airliners will be composite.
For the really long term I think pulse jet powered hypersonic airliners would be pretty neat.
For military fighters/attack planes I predict that the F-35 will be the last major manned fighter development, and pulse jets and scram jets will replace turbojets and turbofans