How can I get tiling windows in GNOME?
It depends a bit what you mean by tiling: Permanently tiling or just temporary to get an overview and select a window? If you use compiz ("Desktop effects") the latter is possible by pressing Super+W (Super is normally the "Windows"-Key). For "permanent" tiling:
Tile windows with compiz:
Install the Compiz Settings manager (e.g. package compizconfig-settings-manager for Ubuntu) and the additional plugins (again for Ubuntu: compiz-fusion-plugins-extra). Then activate the Grid plugin -- then you can use Ctrl+Alt and a number on your keypad to move and resize the window so that it fits an imaginary grid. This allows very comfortable tiling.
Tile windows without compiz:
If you do not use compiz, there is a gnome applet that allows tiling: http://www.giuspen.com/x-tile/
As has been mentioned, Gnome is not a Window Manager, but a Desktop Environment. You can choose from many tiling window managers, such as StumpWM, wmii, or XMonad.
Here is how you use one to replace the default window manager.
From Mikael Jansson(with a little editing by me to make this more general).
If you, like me, use gnome-session 2.3 and earlier, you'll want to add this to your ~/.gnomerc:
If on the other hand you run gnome-session 2.4 and later, you'll have to change a key in the registry:
gconftool-2 --set /desktop/gnome/session/required_components/windowmanager --type string "Window Manager Executable Name"
making sure the binary is in your path.
This will give you Gnome and default theme settings (such as fonts), but with your-favorite-window-manager instead of Metacity.
BlueTile is based on Xmonad but configured OOTB to work well with GNOME (to some degree, it's not as polished as Metacity or Compiz yet...).
GNOME is a desktop environment; it's not responsible for handling your windows. You need to change your window manager, which does handle that sort of thing. There are quite a few tiling window managers for X you can experiment with
As other folks have said, you can use whatever tiling window manager tickles your fancy. Xmonad, however, is one of the few - AFAIK - which advertises GNOME integration and is widely used with it. Well, for some definition of "widely" I suppose.
The applet 'X Tile' can tile your windows from the Gnome panel on demand. It's in Fedora at least and works nicely.