Many websites will proudly say they are secured by SSL, but that just means your browser has a secure connection to their web server while you are uploading your data. What happens to it after that? Some companies with an online presence are being economical with the truth.
They will say your data is stored securely, but what they actually mean is 'stored in a way that is convenient to us', or 'in a way that allows our ancient accounting software to access the data', or 'allows our website to work', or 'we haven't time to do it any other way as our developers constantly firefight problems', or 'the consultant told us to do it like that, we actually have no idea how it all works', or 'secure enough, until we start emailing Excel spreadsheets of your data from one office to another', or 'secure until we keep using the same master password for our database for years, at which point just about everybody who has ever worked here knows it, that's more convenient for our business'.
Having your data in a locked room, separated from the rest of the computer network, jealously guarded by a techie is a pain for most companies. They want quick and easy access.
The trouble is that website security is unregulated. Saying that you 'store data securely' on your website does not mean that an inspector will come knocking on the door wanting to look at your code, databases, web servers etc. It is a self fulfilled declaration.
These data security issues are there because of bad practises, indifference, ineptitude, but this is all before you add in the threat of hackers doing anything remotely clever into the mix. Then things can get really interesting. The lack of basic database security best practices can be exposed. Look how many fell foul of a SQL Server database virus simply because they never bothered to set a password.
While many of these problems are mostly found in small to medium sized businesses, the big players are not immune, as the recent hack of the Sony PlayStation Network shows. The issue also hangs over services set up specifically to the work in the Cloud.
At the end of the day, you have to take the decision on whether the possible bad effects of uploading your data to the Internet outweigh the benefits. With more and more people doing more and more things online it seems inevitable that people will be prepared to take the risk.