To Kill a Mockingbird is all about mockingbirds, even though the actual word is only mentioned three or four times in the novel.  The reason it's a sin to kill a mockingbird is because

mockingbirds don't do one thing but make music for us to enjoy.  They don't eat up people's gardens, don't nest in corncribs, they don't do one thing but sing their hearts out for us. 

Boo has never done anything but try to be kind to the Finch children; he minds his own business and helps when he can; his only sin was being born different.  Tom has never done anything but be kind and helpful to a young woman who clearly needed help; his only sin was taking pity on a white woman.

Atticus is not an obvious mockingbird, as he is neither poor nor black nor an outcast.  Instead, his offense is trying to do the right thing in the face of prejudice and hate.  For trying to right a wrong--"to make music for us to enjoy"--he was spit on and villified, and his children were nearly killed.  That makes him a mockingbird.

Atticus most definitely could be a mockingbird. This bird is nondescript in coloration and yet can imitate or sing many different bird songs. Atticus is not a spectacular looking man, nor does he have any outstanding traits (according to his children) that would set him apart from other dads. Yet he hides the unpleasantness of the world couched in neutral terms when his children ask those difficult questions about life in Maycomb. He does not raise his voice, like a loud crow would. Nor does he scold like a blue jay. In court, his statements are neutral in tone and phrased to fit the mentality of the witness and jury. His bravery and courage was always understated, just as the mockingbird's appearance is. Until he opened his mouth and wisdom poured forth, no one would find him remarkable, just like the grey mockingbird.

Can Atticus from To Kill a Mockingbird be considered a "mockingbird"?

It would be hard to make the argument that Atticus is a mockingbird. Although he does have some of the qualities of a mockingbird, he does not have others. 

First, let's look at what we know about the mockingbird according to miss Maudie:

"Mockingbirds don’t do one thing except make music for us to enjoy. They don’t eat up people’s gardens, don’t nest in corn cribs, they don’t do one thing but sing their hearts out for us. That’s why it’s a sin to kill a mockingbird" (Ch.10).

Atticus only does good things in the book, so we can see that as being like a mockingbird. 

However, there is also an implication that mockingbirds are completely innocent beings, and incapable of defending themselves, so shooting them for no reason would be a sin. Atticus is more complicated than a mockingbird in that sense. He is not a complete innocent and he is certainly capable of defending himself. For these two reasons, it would be hard to say that he is a mockingbird. 

In To Kill a Mockingbird, Arthur "Boo" Radley and Tom Robinson are "mockingbirds". Can anyone else in the story be portrayed as a "mockingbird" as well? Atticus maybe?

Tom and Boo are certainly the main adult human mockingbirds in the story. They exhibit the simple innocence found in the songbird, yet they are men accused of crimes they did not commit who become scorned in the community for their supposed sins. Their lost innocence is not unlike the other human mockingbirds in the story--the children, including Jem, Scout and Dill--and it is one of the main themes of the novel. Atticus, too, can be considered a human mockingbird, though his age and life experiences differ from the others. He is no innocent, having seen his own clients face the death penalty before and suffering life's tragedies such as the death of his young wife. But Atticus does only good for the people of Maycomb, whether as an attorney, legislator, friend or father; yet, his actions are perceived differently by others, and he faces the scorn of some of the townspeople who wish to harm him and his family.

Is Boo Radley considered a "mockingbird"?

Yes. Boo Radley would be considered a symbolic mockingbird because he deals with cruelty even though he is an innocent character who helps others and does not harm anyone. In Chapter 10, Atticus tells his children it is a sin to kill a mockingbird, and Miss Maudie elaborates by saying that mockingbirds do nothing but sing their hearts out for people to enjoy their music, which is why it is considered a sin to kill one. Metaphorically, mockingbirds represent any innocent beings who do not harm or bother anyone. Throughout the novel, Boo keeps to himself, gives gifts to the children, and even saves their lives at the end of the novel. In Chapter 30, Sheriff Tate comments to Atticus that he refuses to tell the community about Boo's heroics because it would bring unwanted attention to Boo. Scout understands Sheriff Tate's comment and compares telling the community about Boo to shooting a mockingbird. She realizes Boo is a symbolic mockingbird and knows excess attention would harm him, which is similar to shooting a mockingbird.