I inherited a bluehost account (I mean literally inherited - the guy died and wanted me to keep his sites going).
The previous owner had mistakenly once (or more than once) sent out an email containing a link to an article (intentionally) but with a whole bunch of email addresses in the 'to' box instead of bcc or as separate emails. Then a year later after I'd taken over the sites, a kenyan correspondent who didn't use the internet much did a 'reply to all' including a genuine question in the email, and without deleting the original content. This was then picked up by spamcop as being a likely spam email and Bluehost responded to that. Not only was the site containing the article referred to in the original link (and 'reply'd email) shut down, but bluehost shut down the whole account so every site went offline.
I would say they were quite reasonable when I managed to track down the root cause of the problem and explain it to them though, and it took about 24 hours to my account re-enabled. However, having all the sites shut down at once was a nuisance.
I also had several sites hosted by Rochen Hosting on my own reseller account. Not long after the bluehost shutdown experience I had an infection on a Joomla site, probably because of a rogue extension, where someone was using my site to phish for bank of america account details, a much more serious problem. They only shut down the specific site with the problem, not any of the others. Rochen also have a twice daily backup system called The Vault if you have a reseller account, and you can control that yourself to restore backups of sites. I've used that when I really needed it. It has been invaluable.
Not long after that I noticed that my sitestalker messages for the bluehost hosted accounts were getting more and more frequent - several times per day sometimes - so i've now moved all my sites to Rochen and they've virtually disappeared. I recommend Rochen highly, but they are significantly more expensive than bluehost. You pays your money...