You can install 64-bit Windows, but if it's in place of a 32-bit installation it needs to be a clean installation due to the vastly different architecture of 64-bit. In other words your programs/files will not be retained.
As for advantages, 64-bit systems are designed to read a lot more RAM, 32-bit is theoretically limited to 4GB (although it's more like 3-3.5GB in practice due to hardware addressing). Thus 64-bit is a more future-proof OS architecture. Also certain programs optimised for 64-bit systems may receive a small performance boost depending on what the program is and how well it's been optimised, e.g. the 64-bit version of Adobe Photoshop CS4 supposedly promises a performance boost of between 8-12% for image rendering, the unofficial 64-bit build of Mozilla Firefox apparently increases the image/webpage rendering speed.
One thing to watch out for with 64-bit however is hardware drivers, you'll need specific 64-bit drivers for all your special peripherals such as wireless mouse, scanner, printer etc. This means that if you cannot get a 64-bit driver for your favourite device, you're done for
(at least until the manufacturer releases a 64-bit driver anyway).
Hope this helps.