I certainly wasn't the first one on the bandwagon, but one of my favorite websites of 2004 was Flickr, the photo sharing site. I've slowly begun migrating some of my older photos onto Flickr, and in the future you can find all my pics at this link. If you join up, add me as a contact and drop me a line so I know to look up your photos.
Perhaps the coolest aspect of Flickr is it's free-text tagging system. Users can attach tags to their photos, and all that metadata allows anyone to browse through everyone else's public photos by tag. Pick a random word and see what photos it summons from the Flickrsphere, or browse a list of the most popular tags.
The site has many other useful features, but the tagging ability is my favorite. For now, an account is free and limited to 10 MB of uploads per calendar month. Upgrade to a Flickr Pro account and your monthly upload quota jumps to 1 GB, among other things. The annual price of $41.77 still feels a bit steep to me, but depending on how the site continues to evolve, I could see justifying that just as a way to backup high res copies of my photos and to offload some storage from my web host.
I'd be very surprised if Flickr survived 2005 without being purchased by one of the Internet alpha dogs: Google, Yahoo, Microsoft, Amazon, eBay. Google owns Picasa, Microsoft could launch something similar internally, and Amazon has an alliance with Ofoto, so Yahoo is the most likely suitor. Yahoo also needs blogging software, so perhaps they'll target Six Apart or one of the smaller, still independent blogging software companies. Photo sharing, like weblogs, are one of the most popular uses of the web, and any company not playing in that space is losing a key piece of user mindshare.
Picasa has been in the news this week because they announced their first rev, Picasa 2, since their acquisition by Google. It sounds like a great photo management solution (Slashdot, to take one site, links to many of the web reviews), an iPhoto competitor, but for now it only works on Windows computers. If you own one, give Picasa a spin.