I'm an EM resident, and I often wear a tie during the day. As an intern, I didn't wear the short coat, but I wear the long coat buttoned up. If I'm REALLY worried my tie will get in something, I just tuck it in between the 2nd and 3rd buttons. Anyone who says anything about infection risk is talking out of their asses. EVEN IF a tie is TOTALLY contaminated, there's no evidence there's an infection risk. As a comparison, when you were a kid, when you got cut, did your mother put your cut under the running water? How many got infected? Tap water irrigation has been shown time and again to be safe, and, yet, were you to culture faucets, you would be just amazed at what grows out (as far as gnarly bugs).
Why do I wear a tie? Looks more professional sometimes, and it's just what I'm accustomed to. In the afternoon, it's hit or miss, but, overnight, I usually wear an open collared shirt (often in a subdued tropical print). About half of my colleagues, and about 40% of all the residents in my program, wear "street clothes" with the white coat while working.
Our department put in a dress code, and it was either scrubs, or dress pants (Dockers qualify) and a collared shirt with buttons (tie recommended, but not required). Always, the white coat. Several people have been busting it, and they're going to get busted.
edit: Ah, I was talking about the ED. As a student, I went with the flow. Rarely did I see a man that wasn't in scrubs that wasn't in a tie (across the board). Even in psych, the few attendings I saw, half wore a tie. Women have a little more leeway, since they can wear a dress or skirt, or pants, and there isn't a great correlate to the tie - whereas one guy, who's on the bottom of the totem pole, without a tie (when everyone else has one) stands out.