Use the Notepad2 Modifications installer. It works on 32 bit and 64 bit.

This Notepad++ wiki page also has a step-by-step guide for Windows XP and Windows Vista which also works on Windows 7.

If you want to make sure you are using Notepad2, go to a file that you would typically use Notepad2 for and right click > properties. Then where it says "opens with", select change and select Notepad2.

As of this post's date, the recommended approach to replace Notepad with Notepad2 on Windows 7 is best described here.

Rename notepad.exe to oldpad.exe and a copy or symbolic link of your replacement to notepad.exe

Just thought I'd throw one into the mix. It's based on the original notepad2 installer script which worked well in Vista. I found it on this forum post.

@echo off
TITLE Notepad2 Install Script for Complete Windows Vista and 7 Notepad Replacement
echo.
echo Notepad2 Install Script for Complete Windows Vista and 7 Notepad Replacement
echo Version 1.2
echo.
echo (c) My Digital Life ()
echo.
echo.
echo.
echo Confirm to apply? (Press Ctrl-C and answer Y to terminate)
pause
echo.
echo.

if exist %Systemroot%\notepad.original.exe goto exist_notepad2_already
if exist %Systemroot%\System32\notepad.original.exe goto exist_notepad2_already
takeown /f %Systemroot%\notepad.exe
takeown /f %Systemroot%\System32\notepad.exe
icacls %Systemroot%\notepad.exe /grant "%username%":f
icacls %Systemroot%\System32\notepad.exe /grant "%username%":f
IF EXIST %SYSTEMROOT%\SysWOW64 (bcdedit.exe -set loadoptions    "DDISABLE_INTEGRITY_CHECKS")
copy %Systemroot%\notepad.exe %Systemroot%\notepad.original.exe
copy %Systemroot%\System32\notepad.exe %Systemroot%\System32\notepad.original.exe  
echo.
echo Original notepad.exe has been renamed to "notepad.original.exe" in its original folder.
echo.
copy %~dp0\notepad2.exe %Systemroot%\notepad.exe /y
copy %~dp0\notepad2.exe %systemroot%\System32\notepad.exe /y
echo.
echo Notepad2 installation is completed. 
echo If no error occurred, Notepad2 will now replace all Notepad functions.
echo.
pause
exit

:exist_notepad2_already
echo.
echo INSTALLED NOTEPAD2  ALREADY!.
echo.
pause
exit

In Windows XP, I used this script from this website to get it to work. You need to perform these registry functions first and place the .vbs script into your C:\Program Files\notepad++ directory,

'// USAGE
'// 1)
'// Navigate to registry key HKLM\SOFTWARE\Microsoft\Windows NT\CurrentVersion\Image File Execution Options\
'//
'// 2)
'// Add new subkey with the name of the executable you want replaced (no path) e.g. notepad.exe
'//     This step is what tells windows to use the replacement exe, to undo simply delete the key you created
'//
'// 3)
'// Create new Sting Value called Debugger
'//
'// 4)
'// Modify value and enter wscript.exe "path to this vbs" e.g. wscript.exe "C:\Program Files\notepad++\npp.vbs"
'//

Here is the VBScript:

Option Explicit

'// Declare variables
Dim x        ' old bad habit, I use this for general temporary variables
Dim W        ' This will be the WSHShell object
Dim sCmd    ' This will be the command to run

'// Create WSHShell object
Set W = CreateObject("WScript.Shell")

'// Set the working directory to the one this script resides in
'// If the target program doesn't care where it is run from then you don't need the following line
W.CurrentDirectory = LeftB(WScript.ScriptFullName, LenB(WScript.ScriptFullName) - LenB(WScript.ScriptName))

'// Set the target executable
sCmd = "notepad++.exe"

'// Skip the first argument but grab all the rest
If WScript.Arguments.Count > 1 Then
    For x = 1 To WScript.Arguments.Count - 1
        '// If the argument contains a space then enclose it with ""
        If InStrB(WScript.Arguments(x), " ") Then
            sCmd = sCmd & " """ & WScript.Arguments(x) & """"
        Else
            sCmd = sCmd & " " & WScript.Arguments(x)
        End If
    Next
End If

'// Run the command
'// The number after the command determines how the window should be initially (google WSHShell.Run)
'// The boolean at the end determines whether this script should run the target then exit or wait until the target exits
W.Run sCmd, 1, False