gistfile1.txt

//Apex Controller code
  public List<SelectOption> filterCriteria{
    get{
      //TODO change the names to labels
      List<SelectOption> options = new List<SelectOption>();
      for(Account a : [Select Name,Value__c From Account Limit 10]){
        options.add(new SelectOption(a.Value__c,a.Name);
      }
      return options;
    }
  }

<!-- VF code -->
<!-- Controller has filter string member variable which this select list assigns the selected value to… -->
<apex:selectList value="{!filter}" size="1">
  <apex:selectOptions value="{!filterCriteria}" />
  <apex:actionSupport event="onchange" action="{!filterAccounts}" rerender="id1,id2"/>
</apex:selectList>