I know this is an old thread, but I thought I'd add a little more detail.
There are a couple places you can do the rotation. If you want to do it on playback (e.g. in the media player), you can't do that in Windows Media Player. But as others have noted, you
can do that in 3rd-party media players like VLC Media Player.
On the other hand, if you are trying to rotate the source video you have to run it through an editor or a converter. For example, let's say you took some video in
vertical portrait mode on a phone, if you import this into a Windows PC it will end up showing as
horizontal video turned on its side.
One option is to use an editor like Movie Maker. In the older versions, you would apply a "Rotate 90" or "Rotate 270" effect to the clip. In the newer version, you add the video to your storyboard, double-click to get to the
Video Tools | Edit tab. On the top you see pair of buttons to rotate the video
left or right. Then save it as a new movie (File > Save Movie). However, there is a big caveat with this method. It will rotate the video but it will still be within a horizontal rectangle. The result is black bars on either
side of your video.
A better solution, is to use a converter that will keep the correct dimensions and won't fit the video into a horizontal rectangle. The easiest solution I have found is to use Freemake Video Converter. Import the sideways video, click
the edit button and choose rotate, choose the desired output (which can be the same as the input or different), then click the Convert button.
Using this last method, you end up with a video that is truly rotated to a vertical orientation (taller than it is wide). It also makes the thumbnail look correct without black bars on the side. And if you pass it around to others, it will stay rotated.
It will also play in the right orientation even in media players like Windows Media Player without needing to rotate it each time on playback.
You're welcome. :)