Thanks, everyone, for the replies.
So since I now know that the 32-bit and 64-bit specs relate to the memory bus size, what would be some examples of why I would want/need a card with a 64-bit bus over one with a 32-bit bus? Are the 64-bit bus cards primarily geared towards gamers, or would more general use like Photoshop or watching high-def video also benefit from having a 64-bit bus on the card?
Really, what it means is anything that is video-intensive, will perform better as you move to a wider memory bus (all other specs being equal).
I do have to say, even a 64bit bus would be terrible for intensive gaming (think: higher/highest settings in most video games, though this is a gross oversimplification). Most recent-generation cards between mid-performance and top-end have over 256bit memory buses, even 384 and 512bit.
[You can also have a 512bit memory bus on a card that happens to perform terribly for games, if the manufacturers coupled that with low-end specs.]
As for needs, well... hard to really say when a specific bus width is better than another.
If you want to do GPU-based video acceleration, a wider bus, like 128bit, will certainly perform better than a 32bit. Anything 3D, and I'd pretty much say you want a minimum of 128bit - gunning for quality settings with recent games, nothing less than 256bit... and that's coupled with a beefier card anyhow.
And yes, intensive use of Photoshop, and more appropriately, any visual-media editor, would be best coupled with a wider bus. Video-editing, GPU-based video rendering, 3D modeling software, and the like... would perform better on a wider bus.
Most importantly, do consider this: you won't see many cards of similar-specs with widely varying bus widths. And there are also architectural differences between GPU generations, where the new-generation top-end card is released with a bus width that is less than the previous model. And it still performs better in every possible way.
Most often, the architecture/design is more important than the specs you are shown.
So, as others stated, it is best to shop by using benchmarks as a reference, than by worrying over specs.
It really is hard to say application Z needs a specific bus and is thus impossible to recommend any video card with a bus less than X.
Because such apps could perform terribly on a card with a 128bit bus, and then turn around and perform beautifully on a card with a 64bit bus.
Some benchmark sites even go and use such photo/video/modeling suites in their GPU benches.