Is it possible to put a C5 engine into a 1968 corvette, four speed, that originally had a 427. Would it fit with hood clearance and would their be any problems to get the vacuum for the wipers and head lights.

Yes it is possible. It will fit under the hood. Just don't use "truck" accessories. Either try to make the C5 serpentine drive or try to find '98-'02 F-body serpentine drive or aftermarket.  There are more and more C3's being re-powered with LS type engines. It is expensive by the time you purchase all the parts and pieces to do the swap.

I'm in the process of swapping a aluminum block L33 5.3L engine into my '81.
 I just had the block bored out to a 5.7L since this is one of the few 5.3's you can safely bore to a 5.7.
This engine is being built very similar to a C5 LS6 spec except for a slightly hotter cam.

To start with, you'll need to buy:
Engine mounts.
PCM w/ wiring harness
Electric cooling fans
Electric fuel pump w/C5 filter regulator
Bellhousing/Clutch assy.w/flywheel
Hydraulic clutch conversion kit. Unless you want to go through the hassle of keeping it mechanical.
Exhaust headers, then modify the exhaust system to make it work.

Then you have to mess around with sensors and sending units to make your stock gauges work and also work with the PCM. Or change all the gauges over to electronic ones that work with. Since your tach and speedo are cable driven you'll need a converter box to convert mechanical to electronic signal for the PCM.

I'm know I'm missing a few things, but this will give you an idea of where to start.

Thanks for the info. It looks to be a much more work than I thought it would be. I really don't want to change the gauges or take away from the interior looks of the 68, I am just wanting a hot dependable engine, and I was thinking maybe a newer model engine with less problems. I have a 350 now and it does not have the power. I could go back with the 427 original engine, but an older engine may have problems. 

If cost is not an issue get a fuel injection set up on a strong crate motor or one you rebuild. The advantage of doing that is MPG and engine operation and management is way more accurate then a motor with a carb.