To begin with, whatever I added has to have a simple interface. Too many bells and whistles can often just be confusing and cluttering. Next, I had to utilize tools that were already part of her routine. I did not want to add steps or things to check. That goes with the last criteria, which is that there had to be automatic notification.
My sister-in-law set her grandma up with a Gmail account a couple weeks ago. That is useful for interacting with Google's products. It is also straightforward to export the content. She set it up to forward the mail to my grandmother-in-law's real account, but Gmail also supports POP and IMAP. I think forwarding is the easiest and most straightforward solution.
Since the Google account was already set up, I set up an account at YouTube so she could see private family videos I share. I also connected her Picasa account with mine so she would see any updates I put there (I do not update Picasa much). She already has a flickr account, which is where I do most my updating. Flickr automatically emails her when I post new photos.
The big "win" for the session was setting up Thunderbird to read RSS feeds of her grandchildren's blogs. Most modern email clients include some type of RSS reader. My grandmother-in-law uses Thunderbird, and it can handle RSS feeds. If she was checking her mail it Gmail I would have used Google Reader.
Not all blogs have feeds, and not all blogs that have feeds make them easy to find. However, if a blogger blog has a feed then it is located at bloggerurl/feeds/posts/default. I just fed those into Thunderbird, and her email client will now say when any of them are updated. For any private blogs, she has to receive email notification (easily set up in Blogger).