Users with Windows Mobile 5 and above can take advantage of Web Video Downloader, although non-touchscreen (Windows Smartphone) users should avoid this app as there is no way to access the on screen menu.
You can grab a copy of W.V.D. Web Video Downloader from FreewarePocketPC.net - the file is 1.3 MB and should be downloaded directly to your Windows Phone or first to your PC and then copied to your mobile device. The app should be installed to your Windows Mobile device memory rather than any expansion card - the storage card is used as the default location for downloading the videos to, so it makes sense to have the main program and the downloaded content on separate drives.
Note also the requirement for the Coreplayer media player or it's freeware ancestor, TCPMP. These or similar products are required to view the FLV, MP4 or other file format used in streaming the content that Windows Media Player Mobile isn't equipped to decode.
Finally, be aware that use of W.V.D. Web Video Downloader will eat into your data plan, so aim to use it either with a generous data usage plan or with a WiFi connection.