Would a late 2008 MacBook run with 8 GB or RAM if correctly purchased? We've got a late 2008 MacBook (already upgraded to 4GB RAM), it's fine -speed wise, but when checking the activity monitor were very close to running out of space -RAM wise.

What I would like to do is upgrade the RAM to 8GB, but checking the Crucial website, it looks like the most RAM I can get in is 4GB. Is this correct or is there a way I can upgrade to 8GB? What would be preventing you using 8GB RAM?
It is certainly possible to install 8GB of RAM on this model. You will need to check if you have the correct Boot ROM Version and install it if needed. Follow this guide.

You can learn what RAM to buy for your MacBook using System Profiler.