Gmail. Damn near everyone you know uses it, and now they (and you) can use it offline. Sound the trumpets! And if that's not enough, offline Google Calendar and Docs will be rolling out within the week. This pleases me.
Offline Gmail has launched as a Google Web Store app for your Chrome browser. If you don't use Chrome you're out of luck for now, but Google says that they plan to make this available in other browsers as well. The UI is taken directly from Gmail's tablet app, and the implementation is very good. It's extremely fast, clean, easy to navigate, and installing it is simple. It's available now, and in the brief time I've spent with it, I'm a fan. In fact, I prefer the dual-pane UI to the default browser version. You can't yet control the number of emails that get synced, but Google says that's coming soon.
The Calendar and Docs apps that are coming out within the week sound good, too, though they won't quite as robust as we'd like right out of the gate. When you're in the offline calendar you can view and RSVP to appointments, but you can't add to them or edit yet. The same goes for Docs. You can view them, but you can't make changes until you have an internet connection again. The Big G says they're working on bringing those missing features soon, and when they do, it will be very sweet, indeed. I'd also like to see them add an implementation of that handy-dandy black bar at the top so I could more easily flip around within my Google Apps (when I'm online).
If you use Chrome you can take Offline Google Mail for a spin now, and look for the other two to be available within the next few days. As someone who has to stay glued to my Gmail more or less constantly, this is great news. [Gmail Blog]