Online/cloud storage -- i.e. keeping your files with an online storage company that allows you to access them from anywhere -- is here to stay. The best known example is Dropbox. The newer kid on the block is Google Drive, which has similar functionality. If you already have your entire world set up with Dropbox, there is no overwhelming reason to switch. However, if you are just starting with online/cloud storage and you have a Google or Gmail account anyway for your other needs, Google Drive is great because it is integrated with all Google apps.
If you are staying with Dropbox and you are worried about security breaches (honestly -- a security breach at this day and age is unforgivable), there are simple ways for you to keep sensitive files -- just encrypt them.
If you want the gold standard in file encryption and are not bothered by less-than-friendly user interface, use TrueCrypt (good how-to link).
If you want a simpler and friendlier program, there are two good choices:
1. Use encrypted zip file -- see link for details.
or
2. Use BoxCryptor -- see link for details.
