Linux Keyboard Hard Remap Keys

Run the command xev. In the xev window, press the AltGr key. You'll see something like

KeyPress event, serial 29, synthetic NO, window 0x6400001,
    root 0x105, subw 0x0, time 966635535, (243,-207), root:(1891,26),
    state 0x0, keycode 66 (keysym 0xff7e, Mode_switch), same_screen YES,
    XLookupString gives 0 bytes: 
    XmbLookupString gives 0 bytes: 
    XFilterEvent returns: False

Note the keycode; since the key isn't doing what you want, you'll see something else (possibly Alt_R) instead of Mode_switch. You want to assign this keycode to Mode_switch, which is X11's name for AltGr. Put the following command in a file called .Xmodmap (note capital X) in your home directory:

keycode 66 = Mode_switch

Additionally, you may need to assign a modifier to Mode_switch, but if all that's happening is a keycode discrepancy there'll already be one. See Set the key for spanish eñe letter for more information.

Run xmodmap ~/.Xmodmap to test your file. On many systems, including Ubuntu 10.04, this file is loaded automatically in the default Gnome environment. On other distributions or environments, you may need to indicate explicitly that you want to run xmodmap ~/.Xmodmap when you log in.

As I've stated in my question, there is already xkb which already has alot options for modifying the keyboard. It wasn't an option for me because the only option to modify the printscr key, replaced it with Win_R. Gunnar Hjalmarsson on this thread suggested to me that I modify xkb's modifications so that the printscr/win_r would do printscr/menu instead. We worked out a solution together and I'm going to retransmit it here:

In terminal, enter:

sudo su
nano /usr/share/X11/xkb/symbols/altwin

At the bottom of the file you will find:

// Win is mapped to the PrtSc key (and the usual Win key).
partial modifier_keys
xkb_symbols "prtsc_rwin" {
    replace key <PRSC> { [ Super_R, Super_R ] };
    modifier_map Mod4 { <PRSC>, <RWIN> };
};

Delete this section and replace it with this:

// Menu is mapped to the PrtSc key (and the usual Win key).
xkb_symbols "prtsc_rwin" {
     replace key <PRSC> { [ Menu, Menu ] };
     modifier_map Mod4 { <PRSC>, <MENU> };
};

To delete in nano, use backspace key (highlighting and deleting doesn't work). To paste, use shift-ctrl-v. To exit and save, press ctrl-x, select yes to overwrite and press enter.

Reboot. In Gnome/Ubuntu Go to gnome-tweak-tools In tweak tools go to Keyboard & Mouse section, press the Additional Layout Options button and expand Alt/Win key behavior. Selecting the option on the very bottom: Win is mapped to printscr (remember that we've modified just this behavior to swap print and Menu instead of print and Win). (I'm sure there is a way of turning on the modded xkb option in KDE but I don't use it, so I can't give you the exact procedure).