Is there a benefit to be had from buying more than 4gigs of memory? Does anything else besides your OS being 64 bit come into play? Does your motherboard play any part?
Your CPU must be 64-bit capable; your motherboard must support that CPU. After that, a 64-bit OS can take advantage of memory greater than 4 gigs.
Is there a benefit? It depends on what you need to do. Of course, more memory means you can run more applications at the same time with less disk I/O (due to swap file activity -- the swap file is used to temporarily move data and code in RAM off-line so that the same RAM can then be used by something else; it's like an overflow device that works both ways). If you're playing video games that involve high resolution graphics or the need to store a lot of data in RAM, such as MMORPGs like "World of Warcraft" or "Ashen Empires" or even non-MMORPG games like "Doom III."
With a 64-bit OS there is a performance advantage because the processor can natively deal with 64-bit values instead of having to deal with them in two parts. This requires fewer CPU cycles, and for some applications these benefits are significant (and sometimes noticable).
The motherboard plays a role as well. If you buy a good one, such as one of Intel's higher-end models, the engineering and components that go into them tend to be better as well (quality-wise, performance-wise, etc.). Sometimes the warranties are longer too, which can be a pretty good indication of how much confidence the manufacturer has in their products (they know how they're built, and what the failure rates are for that particular family of products).
For Windows 7, I find that 4 GBs of RAM is actually a fair minimum for regular business and home use. If more than 4 GBs is supported by the hardware, then I'll install a full 8 GBs. If you run two Windows 7 machines side-by-side that have the same specifications except that one has 2 or 4 GBs of RAM while the other has 8 GBs, and start up the same applications (e.g., Google Earth, OpenOffice.org, and Opera or Firefox) at the same time, the machine with more RAM tends to get things started a bit faster. After using them for a while (e.g., type the same address in Google Earth, open up the same web sites in Opera, and load a few documents in Open Office), the one with more RAM will see a lot less disk activity.
Compared to the cost of replacing a disk earlier, and for the performance gains I typically see (it tends to be more noticeable after the user has been using their machine for a few months and has all sorts of toolbars, background processes/services, and add-ons installed), I find it to be a smart investment to start with more RAM right from the beginning.
The amount of RAM you need depends primarily on the applications you run. If you wish to use virtual machines, 4Gb is probably not enough.
On the other hand, 64-bit OSes are more memory hungry due to how paging works. 64-bit code will use more memory, because pointers will take up 8 bytes instead of 4. Same goes for some other kinds of variables. This means if 4Gb was just enough for you with a 32 bit OS, it may not be enough on a 64-bit OS.
As Randolf has correctly mentioned, there are performance gains to be seen from more ram. Windows can be quite smart about how it uses extra memory, for example caching often used programs so that they load faster.
Personally, I found 4Gb insufficient. At high resolutions (4M+ pixels), certain games like Starcraft II will thrash when tabbing out, even with 4Gb of RAM. Given the lower cost of Ram today, 8Gb sounds about right.