No, triggers are object specific, you can see, the first line of code gives the trigger a name, specifies the object on which it operates, and defines the events that cause it to fire:

    trigger TriggerName on ObjectName (trigger_events) {
       code_block
    }

If you want, you can vote on an existing [idea][1] for supporting multiple objects. 

Additionally, in the [apex triggers best practices][2] guide, you can read further details details on trigger best practices.


  [1]: https://success.salesforce.com/ideaView?id=08730000000aM4JAAU
  [2]: https://developer.salesforce.com/page/Trigger_Frameworks_and_Apex_Trigger_Best_Practices