What do you think of Atticus's reaction to Bob Ewell's challenge in To Kill a Mockingbird? Should he have ignored Bob, retaliated, or done...

Atticus was not the type to fear anyone or get revenge.

Atticus chooses to give essentially no response when Bob Ewell makes threats and spits in his face. He just says he wishes Bob Ewell would not chew tobacco. He believes Bob Ewell is just a bully, and that if spitting in Atticus’s face prevented him from taking out his shame and anger on Mayella, that was enough for Atticus. 

Scout and Jem believe Atticus should have done something, since he was definitely capable. After all, Atticus was "one-shot Finch."

“You know he wouldn’t carry a gun, Scout. He ain’t even got one—” said Jem.

“You know he didn’t even have one down at the jail that night. He told me havin‘a gun around’s an invitation to somebody to shoot you” (Chapter 23).

Atticus believes in being the bigger man. He has a reputation for being honorable, and does not really believe Bob Ewell will do anything, even though Ewell was heard making threats after Tom Robinson's death.

Maycomb had lost no time in getting Mr. Ewell’s views on Tom’s demise and passing them along through that English Channel of gossip, Miss Stephanie Crawford. Miss Stephanie told Aunt Alexandra in Jem’s presence (“Oh foot, he’s old enough to listen.”) that Mr. Ewell said it made one down and about two more to go (Chapter 25).

It seems Ewell believed he was vindicated, but this was not enough. He had a bigger hit list, even if he was just talking. Who were the two to go? It might have been Atticus's children. He had already spit at Atticus.

In hindsight, Atticus probably should have taken Bob Ewell more seriously because Ewell did attack Scout and Jem. If Boo Radley had not rescued them, they might have been more seriously injured or killed. Bob Ewell was clearly dangerous.