Also, I did hear that having an American child (just needs to be born here) makes things easier still.

There are a few more requirements to "just being born here" for a child to have US citizenship, IIRC. I thought I heard somewhere that they were having trouble with illegal aliens coming in to have kids, then going back home, just so that their kids had US citizenship, so they changed the rules for that.

My mom is American, but I was never registered with the US consulate when I was born (so I wouldn't have to face conscription in the future). When my visa ran out here, I just applied for my US passport, which required my birth certificate, my mom's birth certificate, her wedding certificate (I wouldn't have been able to get citizenship if I had been born out of wedlock), plus evidence of her having lived in the US for 10 years prior to my birth (i.e. high school and university transcripts -- tax returns would have sufficed, as well). It took two weeks to get my passport, and now I can't wait 'til November '04, so I can go vote for the most popular person not named Bush.