I have a relative that has accumulated many digital photographs on their PC. What would you advise to preserve these files so they will still have them in a decade or more?
If you want them to be available in a decade, print them, put them in a box, and put the box in the loft. They'll still be viewable, no matter how much technology (or the technology that your relative has) changes in the intervening years.
On the other hand, I'm guessing that you'd like the photographs to stay digital. In this case, the key is making copies and making sure you know when one of those copies has broken. For normal consumer-level backup, I'd recommend leaving the master copy on their computer's main hard disk, then buying an external hard disk to use with your favourite backup software (I highly recommend Time Machine if you're on a Mac, but can make no recommendations for Windows). Back up the whole disk while you're at it, and set it to update the backup at least every day or so. That way, you'll find out if one of the disks fail (and over a decade, they probably will), and you can replace it and restore from the other one. Make sure you set the backup up again every time you change computers, updating the file format the images are stored in if necessary.
If you want to be a bit more paranoid, consider uploading the photos to some sort of online storage, either dedicated to photos (e.g. Flickr) or just general storage (there are lots, with varying costs). That way, you'll still have your photos if the house gets flattened by fire/flood/earthquake/meteorite storm/rampaging elephants.
I recommend to use a service like dropbox.com where your data is stored in the cloud. by "nature" (different data centers, backup, etc.) the stored data is moved around regularly so data won't be lost due to physical failure of hardware.
this service works cross-OS and keeps your data in sync over various computers. -> nice feature: you buy a new computer -> you just install the dropbox client, sign in to your account and your data is synced to the new machine ;)
In terms of losing the digital files, you should look into a decent backup solution.
Personally I have my photos on a raid server, which I take a copy of onto a separate encrypted sata drive that fits into a slot in the front of the machine. That lives in a drawer unplugged except the 30 minutes a month it takes to sync the backup.
I also have an encrypted usb drive which lives at a friends house, with a copy on it which I sync every 3 months.
Finally, I use a crashplan account so it's automatically and continuously uploading changes to a cloud based service also.
I'm fairly sure its safe enough for what I need, but you may want more(or less). I cant recommend dropbox or crashplan type systems enough, but don't overlook physical printouts and offsite backups also.
What you use depends largely on what your fears are and the budget you have. For me, I was worried mostly about accidental deletion (hence the 1 and 3 month fall back points) and also hardware failure (hence raid, 3 copies).
On a budget or for a beginner, I'd recommend dropbox (maybe pay for the bigger quota)but you will need a broadband net connection. Factoring in hardware failure things do get a bit more complicated though.
Finally it depends how much data you're talking about.
If you have a Windows Live ID (or a Hotmail account), you automatically have 25 GB of free storage on Windows Live Skydrive. Consider uploading them to there and one other location, and you'll be fully backed up.
Online/cloud storage will last longer than some of the other options out there, such as CD/DVDs, external hard drives, etc.