I hear others saying that babies get overstimulated, but I do think it is normal to seek out and want eye contact with parents. My ds was like Lindsay's though--he didn't really make eye contact for several months. In the beginning he was very sleepy, so I attributed it to that. Then we noticed one of his eyes turned in and I attributed it to that, so we took him to a ped. ophthalmologist. But he outgrew it by 3 months and the lack of eye contact persisted.
Around 4 months he'd start looking into our eyes but there was never that intent gaze you hear about. He would also turn his head side to side to avoid our gaze. He NEVER made eye contact while nursing, and he nursed for two years. Even now he is very sensitive about a lot of things. I have had him evaluated a couple of times and everyone has concluded that he is a typical kid. He also smiled, laughed, babbled, and talked "on time." And he enjoys pretend play, is loving toward us (on his own terms), and is starting to play well with other kids (he is 4).
I think the smiling and laughing are great signs that all is well but of course as with any baby keep an eye on milestones like babbling, pointing, etc.