I use DO for a messing around on a small web app I'm developing. Within 24 hours of having my droplet up the root password was guessed and my machine was used for some DDoS. Granted I was an idiot for not changing the password immediately but I definitely felt like DO should just use ssh key validation like AWS does right off the bat. That deters attackers from even trying brute force attacks in the first place.
Anyway, I checked the logs and pretty much the minute my machine was deployed a script was guessing my password (lots of failed login attempts for "root" and "oracle"). This probably means someone knows DO's IP addresses and their automatically generated password scheme (all lower case alpha characters of a fixed length).
I reported the incident and destroyed my droplet since there was nothing important on it. When I heard back from DO I basically got (paraphrasing here) "you should install fail2ban next time". Case closed. I'm not a big customer or anything so I don't expect premium support or anything but I feel like someone should have looked into the attack a bit more. Seems like a lot of people are experiencing the same thing.
I guess what I am saying is you get what you pay for (it is only 5 bucks after all).
EDIT: Still using DO. I was just a bit more careful next time I deployed a droplet.