Here's the code,  only one query is made and the results are looped through.  The code seeks to find duplicate Agent_ID__c values before a record is saved (permitting the default value of zero) and notify the user of the record where the value is currently in use.

    public static void CheckForDuplicateAgentID (Account[] objOriginalAccounts, Account[] objUpdatedAccounts) {

        Set<Double> dblAgentID = new Set<Double>();
        List<Account> objAccounts = new List<Account>(); //Set<Account> is not allowed
        Boolean blnAdd;
       
        //We only want to do this work for Accounts that have had Agent_ID__c changed
        for(Integer i = 0; i < objUpdatedAccounts.size(); i++){
            blnAdd = false;
           
            //If the original account value is null,  this is an insert - so run the code anyway
            if(objOriginalAccounts == null){
                blnAdd = true;
            }
            else{
                //If this trigger holds inserts AND updates,  this isn't going to work!  Is this a possiblity?  Not under the current business model
                if(objOriginalAccounts[i].Agent_ID__c != objUpdatedAccounts[i].Agent_ID__c){
                    blnAdd = true;
                }
            }

            if (blnAdd){
                objAccounts.add(objUpdatedAccounts[i]);
            }
        }
       
        //Get all Agent_ID__c
        for(Account objThisAccount:objAccounts){
            //AgentID of zero is permitted as a duplicate
            if(objThisAccount.Agent_ID__c > 0){
                dblAgentID.add(objThisAccount.Agent_ID__c);               
            }
        }
        System.debug('dblAgentID.size(): ' + dblAgentID.size());
       
        //Make a single soql call to search for Agent_ID__c that already exist
        Account[] objExistingAccounts = [SELECT a.Id, a.Agent_ID__c, a.Name FROM Account a WHERE a.Agent_ID__c in :dblAgentID];
       
        //Now loop through the result set
        for(Account objResultAccount:objExistingAccounts){
            System.debug('objResultAccount.Agent_ID__c: ' + objResultAccount.Agent_ID__c);
           
            //Do any of the accounts found match accounts from the trigger on Agent_ID__c?
            for(Account objSentAccount:objAccounts){
                System.debug('objSentAccount.Agent_ID__c:objResultAccount.Agent_ID__c = ' + objSentAccount.Agent_ID__c + ':' + objResultAccount.Agent_ID__c);
                
                //Is there a match on Agent_ID__c?
                 if(objSentAccount.Agent_ID__c == objResultAccount.Agent_ID__c){
                     //Okay,  we're comparing the account record we were sent with the account record we found
                     //If the two have the same ID that's good because it means that we're talking about the same account
                     //If the IDs differ,  we're talking about 2 different accounts. BAD,  notify the user
                    System.debug('objSentAccount.Id:objResultAccount.Id = ' + objSentAccount.Id + ':' + objResultAccount.Id);
               
                     if(objSentAccount.Id <> objResultAccount.Id){
                         objSentAccount.addError('The Agent ID provided (' + objSentAccount.Agent_ID__c + ') is already in use for the following agent: ' + objResultAccount.Name + '.  Try a different ID or set the other one to zero.');
                    }
                   
                    //We got it,  exit this loop to look for the next objResultAccount
                    break;
                }
            }
        }
    }

Thanks for looking!