Note: I realize some of the stuff below is not necessary. I'm only writing what I did and my experience so far.
Samsung Galaxy Nexus arrived Friday afternoon around 3pm (was overnighted). It was chilly out and the SGN box and device were pretty cold. Decided to just let it sit and warm up a little to room temps.
Around 5:30pm I activated over my home phone. I then installed the SIM card and the stock battery. I did NOT turn the SGN on. Instead, I plugged it in and left it alone.
I was up late Friday night so at around 1:30am I disconnected from the outlet and I turned it on and activated. I used a fresh google account (different than the one from my OG Droid) -- I wanted a clean start. I used the phone for a while, just checking out some of the features and hoping around the OS. The only settings I changed were turning WiFi on and brightness off (by clicking options in the power control widget). GPS and sync were on and Bluetooth was off (by default on my phone).
Went to sleep around 2:45am and left the SGN unplugged. Got up Saturday morning around 9 and had a day of general use. Installed the software update, threw a still image on there for the background. Went to lunch with my family, did a little bit of shopping. I used the phone to occasionally snap a picture and upload a photo to Facebook and read a quick article on the net. I was out and about for about 4 hours total.
Battery not looking terrible, while back at home I did not use it constantly but checked it every once in a while and responded to a text or google talk message. Read an article here and there through the news/weather app. Installed a new app every so often.
Later in the evening I watched a few videos on youtube (looked great). I also played with the camera a bit more and tried google video chat which worked nicely. Played with some of the wacky features of the video camera. Throughout the rest of the evening I played with it every once in a while.
It's now almost 3am and some battery info is below.
I was an original Droid owner, really liked that phone. It went through a lot, even came back to life at one point when I thought it was completely dead from the abuse it took. But that's another story.
I do love the SGN so far. It's fast, a great size (I wouldn't have minded it even being a little bigger), and everything works fine so far. I notice a few quirks. The WiFi and overall reception seem slightly worse than the Droid so far. HOWEVER, I will say that there were times my wifi AND cell signal had no bars and I was still able to surf the net and stream video with NO hiccups or noticeable slowdown in speed. Leads me to believe the WiFi signal indicator is a little off.
I've seen a bunch of battery life complaints and perhaps it is bad when you use the phone much more. But for me, so far, it seems fine.