You can, but you will need to do a clean install, an inplace upgrade is not possible when going from a 32 bit to 64 bit OS.
You can save your files and settings using the Windows 7 Easy Transfer Wizard to an external usb drive or second internal drive, or to dvd.
To use the W7 Easy Transfer Wizard:
Browse to the DVD drive on your computer and click migsetup.exe in the Support\Migwiz directory.
Go to Windows 7 Upgrade Advisor to check compatability.
http://windows.microsoft.com/en-us/windows/downloads/upgrade-advisor
Right now I have:
Windows Vista Home Premium
AMD Athlon 7750 Dual-Core Processor 2.7 GHz
4 Ram
DirectX 11
NVIDIA GeForce GTX 260
Is my system compatible with Windows 7 64 bit? If it is, will I have to start a clean install and have everything deleted? Will I be able to save files and folders like important notes and large games?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic