How can I determine the SATA controller version on Windows?

A program called HWiNFO can display the interfaces of your system's HDDs (hard disk drives) and ODDs (optical disk drives).  You can get it here: http://www.hwinfo.com/download.php

There is even a portable application so you don't have to install it.

Look in the "drives" box to see the matching interface.

Edit, (from different user, Rasmus): This shows the bandwidth for the hard drive/SSD/hybrid disk installed! Not the motherboard itself. You can see the description under this program; "Drives", sub-catagory: "Interface" - "Model". Use a program like SiSoftware Sandra (freeware/trial) or PC Wizard (freeware) to check the actual support of your SATA interface. SATA 600 (MBs) (3/III) or 300 (MBs) (2/II).

If you have a SATA II hard drive installed in your computer, this program (HWiNFO) will show "Interface" --> 3 Gb/s (300 MBs) under the category "Drives", but if you use the program "SiSoftware Sandra", you will see under "Mainboard" that the "Maximum SATA Mode" under "Disk Controller" is "SATA600" or SATA III / 6Gb/s (600MBs). If you use PC Wizard 2014 (example version), you will see that, under "Drives" --> "Number of Disk Controllers", the bandwidth will be "6 Gb/s", but if you click on "Number of Hard Disk", you will see that the "Serial ATA Version" is "2.0 - (SATA-300)" for the hard drive.

This is the situation on my laptop, where I have an old 2.5-inch 320 GB hard drive installed, which has SATA II (3 Gbs/300 MBs); but the software (when you look under the right section) shows that the disk controller for the computer supports SATA III (6 Gbs/600 MBs).

In HWINFO, navigate in the device tree to Bus > PCI Bus #0. Under PCI Bus #0, click on the SATA AHCI Controller device. Details about this device will be displayed in the right pane. Scroll through this pane and you will find a heading "SATA Host Controller" with the Interface Speed Supported as follows:

As long as you haven't (sorry if this statement is nauseatingly self-evident) previously swapped out your laptop's hard drive and you're still using the original, maybe this website will help: http://www.drivesolutions.com/index.shtml. I have an old VAIO, and spent about 15 minutes looking up in Device Manager what HDD was factory installed (Fujitsu XXXXXX), and then punched it into google to try to find if any sellers of these fossils posted the Gb/s SATA speed to dx what I should buy. Just scroll down and on the left side there's an option to check your upgrades by model. You could also use http://www.crucial.com/usa/en/advisor which won't tell you what SATA you have, but will tell you what's compatible. And their prices are pretty good, too, if you compare them with the drivesolutions website I posted above.

I read minutes ago on a web browser I shut down (so I can't source it), that as long as your old HD has fewer Gb/s than your new one, as long as it's compatible, the only downside would be failing to take advantage of how fast it COULD run. It will still run. It'll just use 1 or 3 ports instead of, say, 6. Hopefully this helps. I'm learning all this stuff new now, so don't take my word as expert. I'm excited to be doing this all myself in the coming days when I buy my parts. Feel free to reach out to experts in customer service on these parts distribution centers, too, as a prospective buyer. Their guys are much more knowledgeable and might have more thorough (or more correct) information than that which I've picked up on echoes in the internet.