APEX CODE:

public class PageBlockTableSortingCon {
 
   private List<Account> accounts;
   private String sortDirection = 'ASC';
   private String sortExp = 'name';

   public String sortExpression
   {
     get
     {
        return sortExp;
     }
     set
     {
       //if the column is clicked on then switch between Ascending and Descending modes
       if (value == sortExp)
         sortDirection = (sortDirection == 'ASC')? 'DESC' : 'ASC';
       else
         sortDirection = 'ASC';
       sortExp = value;
     }
   }

 public String getSortDirection()
 {
    //if not column is selected
    if (sortExpression == null || sortExpression == '')
      return 'ASC';
    else
     return sortDirection;
 }

 public void setSortDirection(String value)
 {  
   sortDirection = value;
 }
 
   public List<Account> getAccounts() {
       return accounts;
   }


   public PageReference ViewData() {
       //build the full sort expression
       string sortFullExp = sortExpression  + ' ' + sortDirection;
      
       //query the database based on the sort expression
       accounts = Database.query('Select id, Name, BillingCity, BillingCountry, Phone from Account order by ' + sortFullExp + ' limit 1000');
       return null;
   }

}


VF Page:

<apex:page controller="PageBlockTableSortingCon" tabStyle="Account">
<apex:sectionHeader title="Accounts List with Sorting"></apex:sectionHeader>
<apex:form >
<apex:pageBlock title="" id="pageBlock">
    <apex:pageBlockButtons location="top">
      <apex:commandButton value="View" action="{!ViewData}" id="theButton" rerender="pageBlock"></apex:commandButton>
    </apex:pageBlockButtons>
    <apex:pageMessages ></apex:pageMessages>
    <apex:pageBlockTable value="{!accounts}" var="a" rendered="{!NOT(ISNULL(accounts))}">
       <apex:column >
         <apex:facet name="header">   
           <apex:commandLink action="{!ViewData}" value="Account Name{!IF(sortExpression=='name',IF(sortDirection='ASC','▼','▲'),'')}" id="cmdSort">
             <apex:param value="name" name="column" assignTo="{!sortExpression}" ></apex:param>
           </apex:commandLink>
         </apex:facet>
         <apex:outputLink value="/{!a.Id}" target="_blank">{!a.Name}</apex:outputLink>
       </apex:column>
       <apex:column value="{!a.Phone}">
         <apex:facet name="header">
           <apex:commandLink action="{!ViewData}" value="Phone{!IF(sortExpression=='Phone',IF(sortDirection='ASC','▼','▲'),'')}">
             <apex:param value="Phone" name="column" assignTo="{!sortExpression}" ></apex:param>
           </apex:commandLink>
         </apex:facet>
       </apex:column>
        <apex:column value="{!a.BillingCity}">
          <apex:facet name="header">
           <apex:commandLink action="{!ViewData}" value="Billing City{!IF(sortExpression=='BillingCity',IF(sortDirection='ASC','▼','▲'),'')}">
             <apex:param value="BillingCity" name="column" assignTo="{!sortExpression}" ></apex:param>
           </apex:commandLink>
         </apex:facet>
       </apex:column>
        <apex:column value="{!a.BillingCountry}">
          <apex:facet name="header">
           <apex:commandLink action="{!ViewData}" value="Billing Country{!IF(sortExpression=='BillingCountry',IF(sortDirection='ASC','▼','▲'),'')}">
             <apex:param value="BillingCountry" name="column" assignTo="{!sortExpression}" ></apex:param>
           </apex:commandLink>
         </apex:facet>
       </apex:column>
     
    </apex:pageBlockTable>
</apex:pageBlock>
</apex:form>
</apex:page>