How do I set cell value to Date and apply default Excel date format?

http://poi.apache.org/spreadsheet/quick-guide.html#CreateDateCells

CellStyle cellStyle = wb.createCellStyle();
CreationHelper createHelper = wb.getCreationHelper();
cellStyle.setDataFormat(
    createHelper.createDataFormat().getFormat("m/d/yy h:mm"));
cell = row.createCell(1);
cell.setCellValue(new Date());
cell.setCellStyle(cellStyle);

I am writing my answer here because it may be helpful to other readers, who might have a slightly different requirement than the questioner here.

I prepare an .xlsx template; all the cells which will be populated with dates, are already formatted as date cells (using Excel).

I open the .xlsx template using Apache POI and then just write the date to the cell, and it works.

In the example below, cell A1 is already formatted from within Excel with the format [$-409]mmm yyyy, and the Java code is used only to populate the cell.

FileInputStream inputStream = new FileInputStream(new File("Path to .xlsx template"));
Workbook wb = new XSSFWorkbook(inputStream);
Date date1=new Date();
Sheet xlsMainTable = (Sheet) wb.getSheetAt(0);
Row myRow= CellUtil.getRow(0, xlsMainTable);
CellUtil.getCell(myRow, 0).setCellValue(date1);

WHen the Excel is opened, the date is formatted correctly.

This example is for working with .xlsx file types. This example comes from a .jsp page used to create a .xslx spreadsheet.

import org.apache.poi.xssf.usermodel.*; //import needed

XSSFWorkbook  wb = new XSSFWorkbook ();  // Create workbook
XSSFSheet sheet = wb.createSheet();      // Create spreadsheet in workbook
XSSFRow row = sheet.createRow(rowIndex); // Create the row in the spreadsheet


//1. Create the date cell style
XSSFCreationHelper createHelper = wb.getCreationHelper();
XSSFCellStyle cellStyle         = wb.createCellStyle();
cellStyle.setDataFormat(
createHelper.createDataFormat().getFormat("MMMM dd, yyyy")); 

//2. Apply the Date cell style to a cell

//This example sets the first cell in the row using the date cell style
cell = row.createCell(0);
cell.setCellValue(new Date());
cell.setCellStyle(cellStyle);

To set to default Excel type Date (defaulted to OS level locale /-> i.e. xlsx will look different when opened by a German or British person/ and flagged with an asterisk if you choose it in Excel's cell format chooser) you should:

    CellStyle cellStyle = xssfWorkbook.createCellStyle();
    cellStyle.setDataFormat((short)14);
    cell.setCellStyle(cellStyle);

I did it with xlsx and it worked fine.