The falling spheres/balls idea reminds me about a game called gumball (I think that's what it was called).... Atari or Amiga, I can't remember. Basically a giant 'ball machine' in which different color balls fell and your job was to sort them correctly in bins so that you didn't mix colors. If you did, then your supervisor would be pissed, come over, and dump the entire contents of that bin (think quality control

).... There were even multi color balls which you *had* to let fall through - damaged goods. You won each level by meeting quota.
"One idea that would be really cool is a survivor horror game where you get two views: your eye view and the eye view of the creature stalking you. The creature is invisible so the only way to tell where he is is by looking at what he sees. So if you see yourself in his vision get the f*ck out of there."
Except that only one screen can do 3D.
I like the idea about signing/placing your insignia next to your High Score though, that is pretty cool.
I think one of the major benefits from the DS that I see is the fact that you can remove a lot of the info clutter found in many games to another screen. That pretty much makes the screen your playing on "bigger" - a big plus for a portable. Thus you still have a small unit (which protects itself with a clamshell design). A lot of games do this currently with one screen by hiding info until it is needed.
Plus not only can you move the info over, but things you may check regularly (a map). It may be hard for any Metroid Prime veterans, but imagine playing Prime with the upper right map removed - such that you had to hit 'Z' whenever you wanted to check it.
Finally who says that it always has to show a map? I never played animal crossing, but the idea above in this tread sounds cool. However, why not take it a step further? Assuming animal crossing uses a map, show the map on the 2nd screen. In a pause menu, let me choose from either that map, other useful things to see, or a list of ongoing events - such as "my garden". Heh, maybe you'd have to buy virtual webcams to keep and eye on them

. Personally I think the idea is a little taxing on the DS in the technical standpoint, but the bottom line is there could be more than one option for what is displayed in the 2nd screen.