We can show the picklist field value on Visualforce page in a selectlist ( dropdown) using the following code in the controller class:

public class classname {
 public List<SelectOption> selectItemsList() {   
      List<SelectOption> selectOptions = new List<SelectOption>();
      Schema.DescribeFieldResult describeResult = CustomObject__c.PickListFieldName__c.getDescribe();
      List<Schema.PicklistEntry> pickListEntries = describeResult.getPicklistValues();
      for( Schema.PicklistEntry eachEntry : pickListEntries) {
         selectOptions.add(new SelectOption(eachEntry.getLabel(), eachEntry.getValue()));    
      return selectOptions;

In Visualforce page, we can use this using select list tag like this:

<apex:page controller=”classname”>
<apex:selectList value=" " size="1" multiselect="false"  >
<apex:selectOptions value="{!selectItemsList}">

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