"I running windwos Vista 64-bit with 8-GB of ram. Most of my applications are 32-bit applications. How much RAM can VISTA dedicates to 32-bit application?"
64 bit editions of Windows can only attribute a total of 4 GiB of RAM to any single 32 bit virtual memory instance (or application), regardless of your total RAM. The reason is simple, 64 bit editions of Desktop Windows run on the x86-64 architecture, which is a processor architecture capable of running both 64 and 32 bit instructions, limiting 32 bit instructions (or applications) to what 32 bit limits them to, thus, 4 GiB of RAM.
Intel and AMD's specification of PAE does support the x86-64 architecture but the software layer of Microsoft's PAE (the API), called AWE, is not supported on 64 bit editions of Windows, so Windows Vista 64 bit cannot attribute more than 4 GiB of RAM for a 32 bit application.
In fact, true 64 bit architectures like the Intel Itanium processor do not support 32 bit applications. The only reason 32 bit applications work on 64 bit editions of desktop Windows is because the very architecture at its core, called x86-64 (often erroneously shortened to x64), is a hybrid architecture capable of running both 32 bit and 64 bit instructions.
It's also the reason why drivers may not work in 32 bit, but applications will, on Windows Vista 64 bit. The Windows Vista 64 bit kernel is written in 64 bit, and thus, drivers must also be written in 64 bit. If Microsoft would have made the kernel in 32 bit, expanded support would have had to rely on PAE, but drivers wouldn't have had to be re-written. In fact, Apple used that strategy with Mac OS X's transition to 64 bit processors and only its future Snow Leopard will have its kernel in 64 bit.
"I also mistakenly thought a 32bit operating system could only use 4GB, having only 32 address bits to work with. But as you can see from the tables above, 32bit Windows Server 2008 can use up to 64GB of physical memory."
Note however that Windows Server 2008 32 bit uses PAE to achieve this.
"The limit for 64-bit XP is given as 128 GB, while on the support site, http://support.microsoft.com/kb/283247/en-us, it is given as 16 GB!
What is correct, 16 GB or 128 GB?"
Short answer is 128 GiB of RAM.
While Windows XP Pro 64 bit can theoretically support 128 GiB of RAM, driver issues, lack of motherboard support and PAE's Intel technical spec limit to 64 GiB can limit this. Very few 32 bit systems will be built to handle 128 GiB of RAM as the use of a 64 bit operating system becomes much more advantageous in this situation.
I have an article on my blog, Pacoup.com, but you'll have to find it yourself as I cannot link to my own articles on MSDN.