I probably need a primer in genetics...

[ddt]

One more: Wouldn't some recessive traits disappear? Wouldn't a whole lot of green-eyed people have to constantly find each other to keep green eyes going? (To use a possibly weak example.) Is it possible that - using this example - there were lots more eye colors in the past, but all those genes just died out?

Not necessarily. There's nothing inherently bad with recessive traits - it just means they're not phenotypically expressed. To carry on with the eye color example - which in reality is more complicated than just one gene - let's say there's a dominant allele E which produces brown eye color, and a recessive allele e which produces green eye color.

Then someone with a heterozygote genotype Ee - so with one "brown" allele" and one "green" allele - will have brown eyes. However, his/her gametes will have the E allele in 50% of the cases, and the e allele in the other 50%. That means that, if two heterozygote people mate, 25% of their children will have genotype ee, and so will have green eyes. 50% of their children will also be heterozygote, so those will carry on the recessive allele as well.

Now suppose that the trait eye color has no evolutionary advantage either way (neither in finding a mate, nor in own survival chances). Then imagine that at some point in time, 25% of the population is homozygotous brown (genotype EE), 50% of the population is heterozygotous (genotype Ee), and 25% is homozygotous green (genotype ee). If you do the math, you'll see that that is a stable situation, i.e., the distribution of genotypes remains the same over generation. There are other stable distributions, btw.