Personally, if the files are that irreplaceable then why would you trust a company that only exists on the internet to store your files on a server somewhere unknown ? Not to mention what they might do with the data.
An external hard drive is not a good place to store them either. Putting a normal hard drive into a small unvented case, with getting knocked, frequent power cycles and subjects to variation of the +5v USB supply makes their life/reliability less than desirable.
If the files are not going to change ( ie photos, important documents ) then I would burn them to a couple of DVD's, but be aware that the life of consumer burnable optical media is about 5 years, so I would replace the dvd's on a 1-2 yr basis.
Or, the best solution is to find someone with a tape drive and tar them to a tape.
A cloud storage might be part of the solution but you should not regard it as a full one. You always need a plan B