This site frequently recommends unrestrictive fan grills for airflow and silence, and I've taken this in, but looking at the grills I have (on Dells), they look quite free-flowing, so I wasn't too worried.
However, in an excellent show of customer-responsiveness, Antec, as a thankyou for sending them product suggestions, sent me a free FanPal - a USB-powered desk fan for cooling the person rather than the computer. This is basically a novelty 80mm case fan with LEDs. See here for a review and good photos.
Well, at risk of being ungrateful, out of the box it just doesn't work very well, which is probably partly why they're giving them away. You can barely feel the airflow 1ft away. So within 30 seconds I had my screwdriver out and was taking it apart.
Freed from its grills, a much more significant amount of air flows. Even just holding only the relatively open looking back grill next to the fan cuts airflow, by my very unscientific estimate, by about 75%! Don't ask me for units

Interestingly, noise and airflow reduction is worst with a given grill behind (upstream) of the fan. Also, the more restrictive looking front (thin, metal) grill is actually a little less restrictive than the back (thicker, plastic), though just as noisy if placed behind the fan.
I grabbed a wire fan grill, and happily I can confirm that they have a relatively minimal effect on airflow and noise - up or downstream. Good news for those with pets and ankle-biters.
In the end, with its faults, the FanPal is a fun thing to have, especially for free. I expect I'll be cutting out its grills, and probably replacing the fan with something quieter, for next summer. At the least, it's given me a USB pass-through power-tap plug, and a cool little red-green-blue LED strip to play with.
I know all my case fans will shortly have nothing but wire grills protecting them. If this inspires anyone to cut up their case, don't forget this great forum article on metal cutting. It doesn't sound too difficult.