So, back on topic here. Many people don't know that Windows XP came in a 64 bit version. It had VERY little driver support, and for the most part, less than one percent of the Windows XP installs were 64 bit. With Vista, perhaps 25 percent of the installs were 64 bit, a huge improvement compared to XP, but still had 32 bit dominating. Driver support WAS better than 64 bit XP, but there were many devices that had really poor 64 bit driver support. By the time Windows 7 rolled around, things were reversed, with 75 percent or more of the Windows 7 installs being 64 bit.
Now, how this relates to Kies and connecting your phone to the computer. The driver support for 64 bit Vista wasn't great from many companies, and NVIDIA had a HORRIBLE track record for driver quality under Vista. 32 bit vs. 64 bit plays a part, but you also have to think: "If I plug my phone into a USB port, are the USB drivers for my computer good, or do they suck?". I am not talking about the Samsung drivers, which could use a lot of improvement, but I am talking about the actual drivers that let the USB ports on your computer work in the first place. If the Samsung drivers don't interact with the USB ports on the computer properly, you can have a BIG problem showing up.
For those with problems with Kies and getting the computer to recognize their S3, one thing to look into is your computer or chipset drivers for your computer. Are there updates available? On some systems, the USB ports are done in sets, with the front USB ports having one controller, and the back being on another. Older machines might have the front being only USB 1.1 with the USB 2.0 ports on the back of the machine.
The laptop I am on right now has a NVIDIA chipset, not just the graphics, but the CHIPSET, and what I have found is that when I run Kies, and "diagnose connection error", Kies will work ONCE, after it installs the drivers again. If I unplug the phone and plug it in again later, it again won't talk to my phone properly. This is a 32 bit Windows 7 machine that had been upgraded from Vista. The problem is clearly with the way the Samsung drivers are interacting with the NVIDIA USB drivers on the machine. My desktop machine that uses an AMD chipset and was a clean Windows 7 64 bit install has NO problem seeing and talking to my S3. Drivers, and chipsets, and settings...they all need to work together.
There is the further issue that if you are not using an Administrator level account, Kies will not have proper permissions to talk to the USB port to talk to the phone drivers to talk to the phone. You can run Kies as an administrator, but with all the issues, it would be best to just use an Administrator level account(not the same as being signed in as Administrator).
There has been a lot of confusion about what is going on, but the "unrecognized hardware ID" that some people see when they plug their phone in is a SYMPTOM of the real problem, not the real problem itself. Samsung has been a bit poor about addressing the issues people are having, and I just hope 2013 is a better year when it comes to that. Kies 2.5.1.12123_2 is the latest version, and seems to work a bit better than the earlier versions, but it still doesn't solve all the problems.
I hope this helps put the issues more clearly in perspective.
Now, back to one of the overlooked questions. The reason for many to use Kies isn't to sync files or even to transfer them since we have Kies Air and other apps that do the job better. Kies will let you do a firmware update from a computer, and for Jelly Bean(Android 4.1.1 or soon 4.1.2), a number of carriers are not doing "over the air" updates, you MUST use Kies to update to the latest Android version, so getting it working is actually useful. For those on AT&T, we had to use Kies to do the update, and problems with Kies means being stuck on 4.0.4. I am actually helping some people on the east end of Long Island, NY do their updates since MY computers at least are working with Kies.