The answer is not quite as simple as yes / no.
Yes, you can hide your address by using a proxy but that doesn't give you true anonymity, unless you are using an anonymous proxy your IP address can still be found (with only a little digging). If you use an anonymous proxy then whilst your IP address is hidden you must remember that the anonymous proxy server still has logs that could be requested & your IP address found that way if it was important enough to do so.
So, in a nutshell, to hide from your friends or to bypass blocking software, no problem but if you are up to no good :) then there is always a chance of being found out...
If anonymity is that important to you then I suggest that you:
A. learn about anonymous proxy servers (and the different levels of anonymity they can offer)
B. learn to chain proxys
As a quick 'PS' - most people answering this question seem to think that public proxies that can bypass blocking software (gets them to their 'myspace' at school) are anonymous... **THEY ARE NOT** all they do is provide a proxy gateway - not the same thing at all !!
Too many years on 'the dark side' of the web :)