Nearly ten years ago I created a listing on Yelp for my web development and consulting business. In that time I've received no work through that avenue and had largely forgotten it existed save the few times I thought to update my logo there, the address as I moved and some other things here in there. I've had a very similar relationship with my properties on Google+ and LinkedIn.
Don't get me wrong — Yelp is great for a more traditional brick & mortar business I think, but it doesn't make a lot of sense for a consultant. So I decided to bite the bullet and delete it last summer.
As it turns out you can't.. And, despite Yelp's reasoning, that's bullshit.
So I did the next best thing and changed and changed all of the relevant information for my business. Thus, Randy's Pizza Parlor & Crematorium was born.
Companies should always let you delete your data, and if they don't I think we have moral obligation to make that data as useless as possible in protest.