Why would I install a program into C:/ directly?

There is no real technical reason to install something in a folder directly at c:\ or to unzip a driver in c:.
It is even against the Windows software design guides as published by Microsoft.

But:
In case the user needs to be instructed to manually run something in that folder it is convenient to be able to give the user simple instructions.
Like: Open "My Computer", open C:, open [folder] and then open program "setup".
By forcing the path to be fixed like this, it is consistent for all users, which makes life much easier for technical support.
This is very often the case for drivers-downloads. All major manufacturers seem to do it like that.

I have worked 1st-line helpdesk on occasion.
You won't believe how many users download something, unzip it, get a phone-call in between and 15 minutes later can't remember where on their harddisk they put the unzipped files.
Then they call the helpdesk or technical support.
If you are the person handling those calls you very quickly start to appreciate the logic of putting these files directly in C:\

What are the reasons some programs install (by default or even requirement) in C:/ directly, and not, like most, into the C:/Program Files/ folder?

Some developers don't follow standard conventions because they're either unaware or too lazy to do things "right." Many amateur developers will also hard-code paths into their software and/or installers rather than querying the environment (e.g., %TEMP%, %APPDATA%, %PROGRAMFILES%).

Also, why is it so common that drivers are unzipped here? I've seen a lot of Intel, Nvidia, ATI, and Xerox folders in C:/-drives, even though to me it makes no sense at all to default there, and not onto the desktop or other user-specific folders. The files should not be required system-wide, as they are only temporary.

As Tonny suggested, this is partly to simplify tech support, but it's also for your own convenience. When you extract the driver files to a location that's easy to find and accessible to all users, it's also easy for the system to locate the files again if you need to reinstall the drivers. Unfortunately, most vendors do not clean up old files, so you can end up with gigabytes of old driver packages that will never be used again. In some cases it may be more appropriate to extract them to %TEMP% or to the "All Users" account, and some vendors do exactly that.

Although 'most' software and configuration files can handle long directory paths, mixed capitalization, spaces and 'nonstandard' characters, they don't always and tripping up on this in the middle of your work-flow can be a minor hassle..

That Microsoft moved the Users folder to the root directory for Vista and 7 probably is a good indication of how many people prefer the root directory (default "c:") in practice.