I just had the need to switch a 32bit Ubuntu system to 64bit – without reinstalling the whole thing.
Luckily I found this step-by-step howto that worked pretty well:
Migrate/Upgrade Ubuntu 14.04 LTS (Trusty Tahr) GNU/Linux from 32 bit to 64 bit HowTo
Basically, what you need to do is switching the kernel and (at least) all base libraries to the x64 architecutre. Effectively you would try to migrate all packages for which it is possible and just fall back to 32bit compatibility where it is not.
I needed to boot with a live cd on reboot as the system wouldn’t come up. Howtos like this are very handy in that case 
Afterwards, the system is working nicely on x64 