Using the web for (almost) everything...

Photo Albums
flickr.com - For $20 a year, I get unlimited space on their servers for pictures.
Pros: Tags and Albums make photo organization easy. Instant sharing with everyone else who wants to see my stuff.
Cons: I can't store video on flickr (yet), making mixed media events difficult to organize.

Bookmarks & Favorites
del.icio.us - Social bookmarking is so hot right now...
Pros: My bookmarks are on any machine with internet access. Tags on del.icio.us are shared by everyone (and I can use everyone's tags).
Cons: Unless you download addons for your browser, bookmarking a site takes a little work.

Email
Gmail.com - Google Email. I used to use Yahoo! Mail, but I was getting 50-100 spam emails in my Inbox a day (and reporting them as spam didn't help). That may be a side effect of having the same email address for 12 years, but it was out of control.
Pros: The feature that organizes replies and responses to emails is a godsend. Tagging, instead of folders, makes email sorting a completely different affair.
Cons: Tagging, instead of folders, makes email sorting a completely different affair.

RSS
Bloglines.com - I used to use Omea Reader (excellent aggregator!), but always ran into the problem where the feeds I looked at during work would still be marked "new" when I came home. For light RSS users, that's not a problem, but I currently track 136 sites with RSS. When each site makes between 1-50 posts a day, I get tired of manually keeping track of what I've already seen. That's where Bloglines comes in...
Pros: One spot for all my feeds. No manually updating multiple desktop programs. Built-in sections for blogs and clippings help with organizing research. Bloglines also shows you how many other people on Bloglines subscribe to that feed AND has a "related feeds" link so you can find other site feeds on the same subject. Very nice...
Cons: Online only. With Omea Reader, I had everything downloaded to my desktop so I could browse offline. This might not be as much of a problem if you have a mobile data service.

Office Documents
Google Documents - MS Word and Excel documents that you can upload, edit, and save online.
Pros: Edit your documents wherever you go.
Cons: The feature sets of Google Docs are very simple. They cannot replace a full Office Suite for every scenario.

Things I'm still working on:

Music & Entertainment
I don't see my 40GB music collection getting uploaded to a site anytime soon, but I just signed up for a free Locker over at mp3.com. If I pay $40 a year, I can upload every song I own. I'll be checking that out...