It happens with a lot of things. PW owns an NES and an SNES, so that's what he's asking about. I own a Saturn and a Windows box, so that's what I'd be asking about. Etc.
> Is it because many games have the score section displayed as white over black,
> and it tends to remain in the screen?
That's partially true, and many games tend to display their scores in the same areas, so even though you might play a hundred different games, the score area gets used similarly on about seventy of them which wears that area harder.
For the same reason, Windows machines tend to get a taskbar burn (screensaver or no); Sony Trinitron TVs (CRT and projection) tend to get a channel number burn (I don't know if they've changed it with their flat panels).
> Or is it just that with those it's very easy to pause and leave the screen on
> while we go meditate on the white throne?
Unless you're planning on spending a few months there, it's not going to be static long enough to burn the screen. Noticeable burn-in happens over a long period of time. That's why the above examples result in burn-in and this one doesn't.
Really, the main reason people ask about these things is because there's a lot of misinformation about them. Best thing you can do for any monitor is turn the white level down, and it'll increase longevity more than any stressing about keeping the image moving.