Probably not the best, but a few odd ones that stick out for me:

• Vince McMahon - "Stand Back" (from the Piledriver VHS, not the Slammy version everyone knows, this had a recap (or buildup) of the Hogan/Andre feud)
• The one from circa 1990 WCW with Scott "Gator" Hall to Billy Ocean's "When The Going Gets Tough"
• Jerry Lawler - "Wrestling With Girls"
• That 1992ish Roddy Piper one they played on Nitro to set up an angle

That Badstreet cover makes me want to stab my ears out. The drummer is just all over the place.

 

The Fabs getting swole reminds me of Butch Reed's "Body Talk" in Mid-South, which is one of the best worst things I've ever seen.

I'm a video editor, so I obviously adore music videos and talking about them, and any time this question is asked about whacky old music videos I immediately think of the Magnum TA music video to Sweet Dreams by Eurythmics that they played a few times on Mid-South in early 84. It's just awesome - Magnum posing in all his manly glory to appeal to the ladies, riding his bike, hanging out in the bar and making out with multiple random women one after the other, it's just fantastically symbolic of the early era of music videos.

 

In terms of pure effectiveness, the Kurt Angle comeback video to "Clocks" and the Randy Savage tribute video they played on Raw should be mentioned, I thought both were incredible in their own ways.