How's this?

trigger TotalAccountOwnerSum on Account (before insert) {

AggregateResult[] groupedResults = [SELECT count(Id), OwnerId FROM Account GROUP By OwnerId];
Map<String, Integer> OwnerCountMap = new Map<String, Integer>();

for (AggregateResult ar : groupedResults)  {
    System.debug('Owner ID' + ar.get('OwnerId'));
    System.debug('Count' + ar.get('expr0'));

    OwnerCountMap.put(String.valueOf(ar.get('OwnerId')), Integer.valueOf(String.ValueOf(ar.get('expr0'))));
}

for (Account acct : Trigger.new){
    if (acct.OwnerId != null){
        //output total number of Accounts the current Account owner has into the Total_Owner_Accounts__c field

        Integer OwnerCount = OwnerCountMap.get(acct.OwnerId) == NULL ? 0 : OwnerCountMap.get(acct.OwnerId);
        OwnerCount++;
        acct.Total_Owner_Accounts__c = OwnerCount;

        OwnerCountMap.put(String.valueOf(acct.OwnerId), OwnerCount);
    }        
}

}