If you like the idea of storing photos on the Internet so that certain people can get to them, but you don't want just anyone to be able to browse the photos, you can make suitable arrangements by using the photo-sharing site's privacy mode. Flickr and SmugMug, for example, let you mark your photos as private, which limits access to the people you specify.
You could also store your pictures at an online storage service, commonly referred to as "in the cloud." Think of these services as virtual hard drives on the Internet, accessible from any computer. You can give access to anyone you wish, securely sharing high-resolution, print-quality photos with people you know.