WWE.com uses RTMP video streams.
RTMP Flash stream recorders can download both RTMP and HTTP streams. You can use download/capture videos automatically with
Replay Media Catcher (RMC),
WM Recorder and
Jaksta. Jaksta allows you to capture packet from flash player, so you can record and watch at the same time without creating separate threads for watching and downloading.
If you don't want to use commercial software like RMC and Jaksta, you can try freeware
Orbit Downloader,
CooJah + Blader,
TubeMaster++,
rtmpdump.
Note that unless you use software that allows to capture packets from Flash player, you need to stop playing video after its URL was detected by a stream recorder (after you start downloading your video). Otherwise you may get an error downloading.
More:
FAQ: How to record/download/capture/save Adobe Flash .FLV video RTMP stream from embedded player