If you're talking about a video file which has to finish downloading before it will play, then the answer is 'yes'. Either right-click on the link and select 'Save File As' or, once you've downloaded the file, search for its title on your PC. This will locate the temporary folder where the PC is located - just copy it across to a regular folder.
If, on the other hand, you're referring to streaming video (which starts almost as soon as you click on the link and can go on indefinitely) then you can't save this (without special software) because there is no file as such. (Your PC just receives a small amount of data, processes it and then deletes it. While it's processing the first bit, it's receiving the second and so on). Asking WMP or your PC to save this type of video is a bit like expecting your TV to record programmes. It needs some outside help. In this case you need some additional software which takes all of the individual bits of data arriving at your PC and puts them together to create a saveable file. There are plenty of programs which will do this but I don't know of any which are free. This one is an add-on for WMP and seems to be well-regarded by those who know more about these things than I do:
http://www.wmrecorder.com/
Chris