Intel small business marketing blogged in January 2016: "You might be resisting [migrating to Windows 10] because you're worried Windows 10 won't work with older computers. But rest easy, it's backwards compatible, meaning it's designed to work with older and newer computers alike. Upgrading your hardware can be expensive, so start with a free operating system update."
But that's not true, as has been noted on Intel support forums. And Intel Downloads contain no Windows 10 drivers, save for NUCs and Compute Sticks, as well as related BIOS updates and utilities. The strange case of Dr Intel-Jekyll and Mr Intel-Hyde, if you will.
Microsoft is determined to force Windows 10 onto all PCs regardless of whether they have hardware which supports it. Terry Myerson, Executive VP of Windows and Devices Group, blogged that Microsoft will intensify its attempts to force users to convert, even changing the updates to Recommended status which means they will automatically install on most PCs. Microsoft re-releases the updates every month.
Microsoft should have included an upgrade adviser to determine if a PC's hardware would support it. The user should have been given the choice of migrating or not -- opt-in rather than opt-out -- but Microsoft designed the scheme to force it onto as many systems as possible so Microsoft would start making money via its new business model of collecting user data and selling it, much like Google.
A naming convention needs to be addressed. In the not-too distant past, the metallic, square product placed in a motherboard socket was referred to as either a processor or CPU (central processing unit) because there was a one-to-one relationship between the two. Then processors were given multiple CPUs, with "core" being used to refer to an individual CPU. Then many processors were given a GPU (graphics processing unit), also composed of one or more cores (it's common to have 2-3 times as many graphics cores as processor ones). I will only use processor, core, and graphics, with the last referring to all graphics capability in the processor.
The confusion with respect to Windows 10 exists because Intel is three things: a supplier of processors which may or may not have graphics capability, a supplier of chipsets for use on other vendor's motherboards, and a former motherboard manufacturer. The impact to Windows 10 is different for each case.
First, let's consider the processors Intel sells to the consumer market, ending up in retail establishments and OEM products. The core(s) portion of the device will support just about any operating system, but graphics capability is an entirely different story. And just to complicate the situation even further, for OEM processors, Intel supplies generic device drivers which the OEM may or may not customize, either adding or subtracting features.
Intel made a corporate decision to only supply Windows 10 graphics device drivers for 3rd Generation Core (Ivy Bridge) and later processors. Previous generations of graphics, most notably the still-popular 2nd Generation Core (Sandy Bridge) will never be supported under Windows 10. In Intel's support forums this has been stated many times. The policy is officially stated on Supported Operating Systems for Intel Graphics Products. Note that graphics for many older Pentium, Celeron, and Atom processors are not supported on Windows 8.1 or 10. Select the device drivers for 3rd to 6th Generations here and the device drivers for 6th Generation only here.
Mind you, Microsoft does supply compatibility, i.e. generic, drivers for non-supported Intel products in Windows 10, but they won't be optimum and no one will help you debug any problems. When Windows 10 first boots, it will search for proper drivers and not always find them. Audio drivers are often not installed when moving from one Windows version to another, so you will need to install them manually.
So this has an impact regardless of whether your PC has an Intel motherboard or an OEM one. However, keep in mind that for desktops, adding a video card will resolve the issue because then you will not be using Intel graphics. It would also resolve the issue for laptops, but adding a video card is problematic because they are not generally offered for retail sale.
Second, let's consider chipsets. If a motherboard manufacturer wants to use Intel processors, it must also use Intel chipsets. The situation is the same for AMD processors which go hand-in-hand with AMD chipsets. The naming convention for Intel chipsets is that the first number is the series, e.g. a Z77 is a 7-series. As with OEM processors, Intel supplies generic device drivers which motherboard vendors can modify. However, Intel does not intend to release chipset device drivers for 6-series and all previous generations for Windows 10. For example, the ASRock H61M-DGS supports Windows 10 because ASRock created device drivers for it (I'd want to test it before I ran production software on it, however). But then look at the BIOSTAR H61MGV3 which only lists device drivers for the on-board LAN.
Third, let's consider Intel motherboards. Intel left the business in 2013. This decision has caused a great deal of confusion because other motherboard manufacturers -- the large ones are Gigabyte, ASUS, ASRock, MSI (Micro-Star International), and Biostar -- remain in business. Intel decided not to support Windows 10 on any of its motherboards because it could reassign or eliminate all of the employees working on them. Windows 10 device drivers for these boards are problematic because Intel will not spend the money it would take to qualify them. Intel has provided non-supported Windows 10 device drivers as follows (remember that Intel changes its website without notice): wired networking, Rapid Storage Technology, chipset, and others via Intel Downloads. The ME (Management Engine) driver for 3rd Generation Core and later processors can be found here. One retired Intel engineer stated that ME drivers are only necessary for systems with AMT (Active Management Technology) or TPM (Trusted Platform Module), though Device Manager will display an error that can be safely ignored. Audio device drivers are actually supplied by Realtek and they can be found on its website.
In other words, you are mostly on your own for older hardware. If you see the classic message KMODE_EXCEPTION_NOT_HANDLED -- no longer a BSOD, but a system crash nonetheless -- you have device driver problems and there might be no solution other than to revert back to Windows 7 or 8/8.1.
The reality is that Intel boards are a crapshoot with respect to Windows 10, with newer boards being more likely to support it. In comparison, all other motherboard manufacturers have added support for it to some degree, with the newer the board the more likely it is that full support is offered. Both NVIDIA and AMD/Radeon have released drivers for Windows 10, but given that Sandy Bridge and older processors are not supported on Windows 10, even adding a video card might not solve the problems.