"White wine with white flesh, Red with red"- is at the very least, antiquated.

If a very simple rule of thumb needs to exist it would be better off saying "White with Light and Red with Rich". Preparation and sauce are more important than what is being cooked with Game being a notable exception.

Oil and vinegar. The acid of the vinegar cuts the unctuousness of the oil and vice versa. Apply this to wine and you end up with acidic wines like Pinot Noir with oily foods like salmon. This principal is very important and is one of the least touted by others. 

Food and wine, like wine itself is a balance (much like life). Although in this case opposites do balance such as a lightly sweet white (i.e. Auslese, LH Chenin Blanc, etc...) with very spicy food of any type, never underestimate pairing similar flavors. Pinot Noir stands up quite well to lemon, no doubt the high acids in each are complementary.

Match flavors. This is so simple that it is often overlooked. The grapefruit/citrus taste of Sauvignon Blancs goes with fish as well as and for the same reason that lemon does.

Avoid wines that are predominated by non-food flavors. Oak is not a taste you expect to find in food. Save oaky wines for fireside chats and other non food events.

Don't be afraid of a little sugar. Most Americans love sweetened ice tea and other 'soft drinks'. A slightly sweet wine, be it California Gewurztraminer, a German Spatlese, or an Anjou from the French Loire, is sure to be a crowd pleaser when served with the right food (say acidic or hot food).

Never pair a wine with any food that is sweeter than it. This makes the term Dessert Wine to be a misnomer. Most sweet wines are best enjoyed after dessert. Some swear by Chocolate and Cabernet Sauvignon, which violates this rule. Try it for yourself sometime (and then try a Black Muscat like Quady's Elysium).

Above all other considerations, drink wine to enjoy it and the company you are sharing it with. Food and wine pairings are elusive and to some degree mythical. Drink wine you like with food you like, but never stop experimenting.