Compose,o,c will produce ©.
You can view the combinations in your locale's Compose file, e.g.
For those without a compose key configured (it isn't by default), the setting is hidden away at System > Preferences > Keyboard > Layout > Options... > Compose Key Position. I prefer to use the "menu" key as compose, but it's a matter of preference.
AltGr (Third-level modifier)
On a UK English layout, AltGr+Shift+c also produces ©.
The standard USA layout doesn't include many characters at the third level as US keyboards have a second Alt rather than AltGr.
The layouts "USA International (AltGr dead keys)" and "USA International" have © at AltGr+c. "USA International (AltGr dead keys)" would be better for most as the other turns the apostrophe into a dead key for the acute accent.
The Ubuntu documentation has a comprehensive list of Compose key sequences plus further info on Compose and AltGr.