Say I want to type the copyright symbol, not something I do every day, not something worth its own key on my keyboard. I type Compose O C and it gives me: ©, Compose ~ ~ gives me ≈,

The built-in shortcuts are very easy to guess, it's great for things I don't type every day. Plus you can add or remove shortcuts so you can change your layout on the fly.

It's great in Windows, Compose is great in Linux, and it's also is a good alternative for the otherwise useless CapsLock key.