Why would dropbox be any safer? Safety/security of email depends greatly on which email system/service you use. If you use a web-based one, then sending it to yourself is technically no different than dropbox. Some corporate email systems are very secure, and some are horrible. It Depends(tm)

What about a USB key? Encrypted, if you're really worried about it

Personally, uploading copies of everything (especially everything at once) to a server/website/whatever strikes me as a greater liability than keeping a backup card or two in a separate pocket or bag. It creates more ways for your documents to be stolen, but it also ensures you have access to them (copies) if you need them. It's a tradeoff--of what are you more afraid, having to cancel all your cards if the originals (or the copies!) get stolen, or finding yourself with no money, no passport, and just a digital copy of your credit card--AND having to cancel it anyway?

Best just not to lose 'em, eh?