Q:

When does a verb not need an object? 

When do you just say "He plays" instead of 'He plays computer games", "He plays tennis"? 

A:

When you want to express the general action as a whole and expressing detail is unimportant or undesired, you don't use an object. 

Person1: "What a cute baby!   Is he fussy?"   
Mother: "No not at all!   He plays, he eats, and he sleeps!" 

Another example (It speaks!): 

Scientist #1: "Let me show you my new invention."   
Scientist #2: "Ok."   
Scientist #1 pushes a button.   The machine emits some warbling sounds: "wrrbl wrrbl hmm grrr... bbuble..smthing...who?...how?...bababa..baby.."  
Scientist #2: "It speaks!"   <--------- (As opposed to, "It speaks English!") 
Scientist #1: "Yes, it does."