How can I save a screenshot directly to a file in Windows?

Little known fact: in most standard Windows (XP) dialogs, you can hit Ctrl+C to have a textual copy of the content of the dialog.
Example: open a file in Notepad, hit space, close the window, hit Ctrl+C on the Confirm Exit dialog, cancel, paste in Notepad the text of the dialog.
Unrelated to your direct question, but I though it would be nice to mention in this thread.

Beside, indeed, you need a third party software to do the screenshot, but you don't need to fire the big Photoshop for that. Something free and lightweight like IrfanWiew or XnView can do the job. I use MWSnap to copy arbitrary parts of the screen. I wrote a little AutoHotkey script calling GDI+ functions to do screenshots. Etc.

You can code something pretty simple that will hook the PrintScreen and save the capture in a file.

Here is something to start to capture and save to a file. You will just need to hook the key "Print screen".

using System;
using System.Drawing;
using System.IO;
using System.Drawing.Imaging;
using System.Runtime.InteropServices;
public class CaptureScreen
{

    static public void Main(string[] args)
    {

        try
        {
            Bitmap capture = CaptureScreen.GetDesktopImage();
            string file = Path.Combine(Environment.CurrentDirectory, "screen.gif");
            ImageFormat format = ImageFormat.Gif;
            capture.Save(file, format);
        }
        catch (Exception e)
        {
            Console.WriteLine(e);
        }

    }

    public static Bitmap GetDesktopImage()
    {
        WIN32_API.SIZE size;

        IntPtr  hDC = WIN32_API.GetDC(WIN32_API.GetDesktopWindow()); 
        IntPtr hMemDC = WIN32_API.CreateCompatibleDC(hDC);

        size.cx = WIN32_API.GetSystemMetrics(WIN32_API.SM_CXSCREEN);
        size.cy = WIN32_API.GetSystemMetrics(WIN32_API.SM_CYSCREEN);

        m_HBitmap = WIN32_API.CreateCompatibleBitmap(hDC, size.cx, size.cy);

        if (m_HBitmap!=IntPtr.Zero)
        {
            IntPtr hOld = (IntPtr) WIN32_API.SelectObject(hMemDC, m_HBitmap);
            WIN32_API.BitBlt(hMemDC, 0, 0,size.cx,size.cy, hDC, 0, 0, WIN32_API.SRCCOPY);
            WIN32_API.SelectObject(hMemDC, hOld);
            WIN32_API.DeleteDC(hMemDC);
            WIN32_API.ReleaseDC(WIN32_API.GetDesktopWindow(), hDC);
            return System.Drawing.Image.FromHbitmap(m_HBitmap); 
        }
        return null;
    }

    protected static IntPtr m_HBitmap;
}

public class WIN32_API
{
    public struct SIZE
    {
        public int cx;
        public int cy;
    }
    public  const int SRCCOPY = 13369376;
    public  const int SM_CXSCREEN=0;
    public  const int SM_CYSCREEN=1;

    [DllImport("gdi32.dll",EntryPoint="DeleteDC")]
    public static extern IntPtr DeleteDC(IntPtr hDc);

    [DllImport("gdi32.dll",EntryPoint="DeleteObject")]
    public static extern IntPtr DeleteObject(IntPtr hDc);

    [DllImport("gdi32.dll",EntryPoint="BitBlt")]
    public static extern bool BitBlt(IntPtr hdcDest,int xDest,int yDest,int wDest,int hDest,IntPtr hdcSource,int xSrc,int ySrc,int RasterOp);

    [DllImport ("gdi32.dll",EntryPoint="CreateCompatibleBitmap")]
    public static extern IntPtr CreateCompatibleBitmap(IntPtr hdc,  int nWidth, int nHeight);

    [DllImport ("gdi32.dll",EntryPoint="CreateCompatibleDC")]
    public static extern IntPtr CreateCompatibleDC(IntPtr hdc);

    [DllImport ("gdi32.dll",EntryPoint="SelectObject")]
    public static extern IntPtr SelectObject(IntPtr hdc,IntPtr bmp);

    [DllImport("user32.dll", EntryPoint="GetDesktopWindow")]
    public static extern IntPtr GetDesktopWindow();

    [DllImport("user32.dll",EntryPoint="GetDC")]
    public static extern IntPtr GetDC(IntPtr ptr);

    [DllImport("user32.dll",EntryPoint="GetSystemMetrics")]
    public static extern int GetSystemMetrics(int abc);

    [DllImport("user32.dll",EntryPoint="GetWindowDC")]
    public static extern IntPtr GetWindowDC(Int32 ptr);

    [DllImport("user32.dll",EntryPoint="ReleaseDC")]
    public static extern IntPtr ReleaseDC(IntPtr hWnd,IntPtr hDc);
}

Update Here is the code to hook the PrintScreen (and other key) from C#:

Hook code

There is no way to save directly to a file without a 3rd party tool before Windows 8. Here are my personal favorite non-third party tool solutions.

For Windows 8 and later

+ PrintScreen saves the screenshot into a folder in <user>/Pictures/Screenshots

For Windows 7

In win 7 just use the snipping tool: Most easily accessed via pressing Start, then typing "sni" (enter). or then sni enter

Prior versions of Windows

I use the following keyboard combination to capture, then save using mspaint. After you do it a couple times, it only takes 2-3 seconds:

1. Alt+PrintScreen
2. Win+R ("run")
3. type "mspaint" enter
4. Ctrl-V (paste)
5. Ctrl-S (save)
6. use file dialog
7. Alt-F4 (close mspaint)

In addition, Cropper is great (and open source). It does rectangle capture to file or clipboard, and is of course free.