I always loved the installation screen that Metal Gear Solid 4 used for it's PS3 version. It showed a dynamic mesh of Snake smoking a cigarette while it gave informational text(and some times quite entertaining text) as it showed an install bar.

It wasn't interactive, but it was sure fun to watch and read as I waited for the game to install :)

A video of the screen can be seen

">here.

Just a note regarding minigames on a loading screen:

Namco holds the US patent on minigames in loading screens (http://en.wikipedia.org/wiki/Loading_screen). What exactly constitutes a "minigame" or "loading screen" is a bit vague (I haven't read the actual patent).

I don't like mini-games - they're distracting and break immersion. Something relevant to the core game is a better option. If your game has customizable character development then loading screens would be a good time to plot your choices. If not, some story, map overview, recap, foreshadowing, practice or anything else related to the player's immediate goals would probably work.