I only take photos for myself and for a Facebook page that I run, as well as some websites. There is no filing system including many clients. If there was, however, the folder structure (in point 1) would change but my backup strategy would remain at least the same or be tightened with adding a backup of disk 3 (point 4).
Coming from IT, where we say that files backed up once (or even twice) don't exist, I know losing your most precious photos is a real possibility. I've been through a few HD failures, on laptops, PC's and external, so I'm not taking any chances. Trust me, it's stuff of nightmares.
1. I use Lightroom to import everything on my PC, where it is set up to COPY photos from my memory card into E:/Photos. The folder system is as follows.
2011 (YYYY)
--2011-01 (YYYY-MM)
-- --2011-01-01 (YYYY-MM-DD)
-- --2011-01-02
-- --... and so on for each day of month
--2011-02
--2011-02
--... and so on for each month of year
2012
--2012-01
-- --2012-01-01
-- --... repeat subfolders for each day of month (2012-01-02 through to 2012-01-31)
... repeat subfolders for each month (2012-02 through to 2012-12)
Lightroom can organise this for you. I googled and found how to do that. You set it once and it self-organises on each import. The reason for this date format is it's easy to sort in Explorer. Even if I copied day folders only for a various months and years, say 2011-04-31, 2011-05-01, 2011-05-02, 2015-06-28, I could sort them by date chronologically, while if they format was dd-mm-yyyy, the operating system (well, Windows, anyway) would not be able to sort chronologically but only alphabetically which is useless to me.
Until I create my second backup, I do not format my memory card. So, if it's full, I either start a new memory card or import and create a second backup, and only then format the memory card. This is because if my computer goes bust (trust me, it's a real possibility), I still have all the photos that are not on 1TB USB 3 disk (second backup disk) - they are still all available on my memory cards).
2. Second backup is on a 1TB USB 3 hard drive (nice and fast) using AllwaySync software (inexpensive and reliable). I back up the whole folder structure above to the disk. The softward will sync the files, i.e. it'll leave files that are the same intact, it will overwrite files you've modified (e.g. changed metadata or applied adjustments), it'll delete the files you have deleted from your computer (such as rejects), and it'll write anything new, comparing the whole file / folder system for you.
3. Third backup is from 1TB USB 3 disk to 2TB USB 2 disk (something that I have from years back). I still use AllwaySync but because of the larger capacity here I don't propagate deletions. Thus, all the new files will be written, all the modified files overwritten, but all of the deleted files will be left. I can delete them at any time and, as it's a 2TB disk, space will not be a problem for some time. It ensures that if I deleted something from my computer by accident and propagated the deletion to disk 2, disk 3 would still contain all those old files, even after a year or five, I could go there and find them.
4. That's it. But, ideally, I would have an exact copy of the third backup.
I use Dropbox but not for backing up my photos. It's more for backing up work in progress, such as if I'm working on photo books, creative projects, typesetting stuff, optimising for web... All workflows are backed up to Dropbox. This means that I can quickly share with people if I need to. I also run a FB page and I have to optimise photos for that and up load 2-10 or so photographs daily. For that, I use just PC's library folder Pictures, and back that up alongside My Documents, Videos and stuff like that, once a month or so, to a different drive, also using AllwaySync software.
I hope it helps.
Oksana