Do You Unplug Equipment During Thunderstorms?

No. I have a Shunyata conditioner and whole house breaker. 

I had a strike near my house once. Audio system survived but the HDMI port on the TV was fried. DVR it was connected to was OK. Moved cable to another port and I was back in business. I have since moved house and I can’t remember what I did with that TV.

I do when im home and know it is coming.

It may help to preface this by saying I live in South Carolina near the ocean and we have severe storms roll through here yearly.   For this and other reasons I'm paranoid about lightning protection. 

Yes, I turn off my power conditioners and sometimes even my breakers but only when I know well in advance what will happen.  The problem is that about 2/3rds of the power issues this house goes through are not even lightning related.   When it is, sometimes I see my lights flash several seconds before I hear the thunder.  It's already too late.  Sometimes I'm away from home when lightning rolls through.

My point is, yes, I do turn things off (not actually unplugged) but I also rely on state of the art surge protection.  I wrote about my thinking at length here and here.

I have a whole house surge protector. My computers and NAS are connected to UPS devices. I turn off my listening room system, NAS, and computers, and pray everything else is protected.