Keep it on a flash drive and have it stapled to your arm if you want to transport it. For images that you want to share, or files that you kinda dont give a rats about if they were to get compromised or disappear, place them in places on the internet that match their confidentiality requirements (email - for secure, dropbox - for kinda secure or your own private server - for very secure)
I think arguing whether a new solution is required because dropbox can't do the job or whether dropbox can keep your files safe is a moot point. If your files are on the internet they are never 100% safe. Just keep your most private files on an external hard disk and have that disk detached from your computer and the only risk you run is if someone robs your house.
I personally think dropbox is great for what i use it for, i put images that i want to share, i transfer files to friends overseas and we all happily share our stuff easily and seamlessly and if i wanna access it i login through the browser or install a new client. WIN. No other service at the moment does it this easily for me. If any of my files where compromised, well whatever, a few holiday pictures or some itineraries.
The legal responsibility is put on Dropbox to keep your stuff safe, but I think the "common sense" responsibility is put on the user to decide whether s/he thinks dropbox is the place for a specific file.