Editing the default keybindings file,

~/Library/KeyBindings/DefaultKeyBinding.dict

Create the directory and / or the file if they're not already there, and make it look like this:

{
/* Remap Home / End to be correct :-) */
"\UF729"  = "moveToBeginningOfLine:";                   /* Home         */
"\UF72B"  = "moveToEndOfLine:";                         /* End          */
"$\UF729" = "moveToBeginningOfLineAndModifySelection:"; /* Shift + Home */
"$\UF72B" = "moveToEndOfLineAndModifySelection:";       /* Shift + End  */
}

If there are already entries in DefaultKeyBinding.dict, just add the 4 new mappings above to the main section of your file.