Apple - Can I change the behavior of the Home and End keys on an Apple Keyboard with Numeric Keypad?

One option is to create ~/Library/KeyBindings/ and save a property list like this as ~/Library/KeyBindings/DefaultKeyBinding.dict:

{
  "\UF729"  = moveToBeginningOfLine:;
  "\UF72B"  = moveToEndOfLine:;
  "$\UF729" = moveToBeginningOfLineAndModifySelection:;
  "$\UF72B" = moveToEndOfLineAndModifySelection:;
}

Quit and reopen applications to apply the changes. Note that DefaultKeyBinding.dict is not supported by some applications like Xcode or Firefox.

In Terminal you can assign home (↖) to control-a and end (↘) to control-e from Preferences > Settings > Keyboard. That will leave you with no key combinations to scroll to the top or bottom of a window though.

It might be easier to just use the default keybindings. In most native text views:

• control-A or option-up goes to the beginning of a paragraph
• control-E or option-up goes to the end of a paragraph
• command-left goes to the beginning of a line
• command-right goes to the end of a line

Another option is to enable the "Use PC Style Home/End" setting in Karabiner (formerly KeyRemap4MacBook):

The setting is defined in Resources/include/checkbox/for_pc_users.xml.

You can also save a file like this as ~/Library/Application Support/KeyRemap4MacBook/private.xml:

<?xml version="1.0"?>
<root>
  <appdef>
    <appname>HOMEENDIGNORE</appname>
    <equal>com.microsoft.Word</equal>
    <equal>com.microsoft.Powerpoint</equal>
    <equal>com.microsoft.Excel</equal>
    <equal>com.vmware.fusion</equal>
    <prefix>com.vmware.proxyApp.</prefix>
  </appdef>
  <item>
    <name>homeend</name>
    <identifier>homeend</identifier>
    <not>HOMEENDIGNORE</not>
    <autogen>__KeyToKey__ KeyCode::HOME, ModifierFlag::NONE, KeyCode::A, VK_CONTROL</autogen>
    <autogen>__KeyToKey__ KeyCode::END, ModifierFlag::NONE, KeyCode::E, VK_CONTROL</autogen>
    <autogen>__KeyToKey__ KeyCode::HOME, VK_SHIFT | ModifierFlag::NONE, KeyCode::A, VK_CONTROL | VK_SHIFT</autogen>
    <autogen>__KeyToKey__ KeyCode::END, VK_SHIFT | ModifierFlag::NONE, KeyCode::E, VK_CONTROL | VK_SHIFT</autogen>
  </item>
</root>

Then open the KeyRemap4MacBook application, press the ReloadXML button, and enable the setting. See https://pqrs.org/macosx/keyremap4macbook/xml.html.en for more information.

Since this answer ranks well in search engines, I want to explain how I did it with the latest version of Karabiner.
The "Use PC Style Home / End" setting has to be downloaded from their website. You will want to go to "Complex Modifications", then "Add Rule" and then choose "Import more rules from the Internet". It will take you to this website: https://pqrs.org/osx/karabiner/complex_modifications/ where under "Emulation Modes" you can find "PC-Style Shortcuts". Once you click "Import into Karabiner-Elements", you can just activate it and are ready to go
You will only need to choose "Add rule" and find the "Use PC Style Home / End" setting right there.