You are not absolutely required to do either- that is, either to use the copyright symbol (c) or say "Copyright ___[date and claimant]"- to protect your work. Since passage of the Copyright of 1976, copyright attaches automatically to an eligible work upon its creation. (Between 1909 and January of 1978, which is when the 1976 Act took effect, you WERE required to affix a copyright symbol to a work in order for copyright to attach. That is no longer the case.)
It is nonetheless advisable, as a practical matter, to either affix the symbol or write out the words "Copyright ___ _____" on a work. The reason? It makes it clear to all of those reading or viewing the work that you are aware of your rights under the Copyright Act and will not hesitate to assert them if someone infringes your rights. Writing out the word "Copyright" is just as good as using the symbol (c). One does not give your more advantages than the other. You should also of course note the year and the name of the copyright claimant. That is, the person claiming ownership of the copyright.
Disclaimer: This answer does not establish an attorney-client relationship or constitute legal advice. It is for general informational purposes only.
Under the U.S. Copyright Law, there is no requirement to use the (c) symbol or to say Copyright 2010 XYZ All Rights Reserved. The only additional value is that it gives notice to potentially infringers about who owns the copyright.
The purpose of using the C in a circle (or the word copyright, which is the same thing) is to give notice to the world that you're claiming copyright rights in the work. There's no requirement that you use either form of notice, but it's a good idea.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
You can use the word "Copyright". "All rights reserved" is, for all practical purposes, unnecessary.
Please see "Copyright Protection in One Easy Lesson" at http://dana.sh/afM75p.
Disclaimer: This post does not constitute legal advice and does not establish an attorney-client relationship.