So I have a Logitech C910 which has since been succeeded by the C920. I didn't pay anywhere near the list price for it though because I got it on a Black Friday sale a few years back. I invested a bit more in my camera because back then it was my primary point of contact for my girlfriend and some friends who live around the country.
That being said, I'm a big fan of the Logitech brand and the C910 was my second Logitech camera. In terms of budget webcams, I have heard good things about the C310: Here Oddly enough it looks like it might actually be the deal of the day for about $15 off of what Amazon usually sells it for (you can see that info here: Price Tracker)
The Microsoft Lifecams Here are nice too, but a bit more expensive and I've had a little more trouble with those. My girlfriend has a Lifecam and the picture quality is great, but for whatever reason her computer has trouble detecting it. In order to make it work she has to unplug and replug the camera each time she boots her PC. I'm not saying that's common, just an issue I've personally been involved with.
Microsoft makes a good webcam.
http://www.amazon.com/dp/B009CPC6QA/
I routinely use mine in a dark room, and it has no problem, at all, in low light situations. I also have it sitting in top if my monitor, and it has no trouble picking up my voice if I lean back in my chair.
Mine started having problems after a few months. There was a short in the cable right near the USB plug and when I would turn the camera around to show my room it would drop out. The proctor would make me start the verification over when the camera cut out.
I use a Microsoft Lifecam that costs about $45 instead.
Microsoft LifeCam Cinema, Retail https://www.amazon.com/dp/B009CPC6QA/ref=cm_sw_r_cp_api_i_6TDtEbXAM9KS7