So here's my horror story with Verizon and the Galaxy Nexus. I got my first Nexus back at the beginning of May. I paid $200 for the upgrade as I wanted a top of the line phone. What I've received, however, has been the bottom of the barrel. I've read that the Nexuses only cause problems in certain states. If that's the case, I'm in SC. I've dealt with store employees (they were pretty good to deal with for the most part), and I've dealt with Verizon customer service (who again have been VERY polite and seemingly understanding for the most part). I, however, am now fed up and will push all my friends and relatives to other services. Oh..and for the record, I am an EXTREMELY patient and low-key person. When you-know-what hits the fan, I tend to just smile and laugh and deal with it as it comes. As it continues to hit the fan, I tend to laugh even more. I can be pushed very far before I let something get to me. So here's the timeline in a span of 4 months
First Nexus - The 4G connection would work maybe 25% of the time. The battery would run down 1% a minute. As I stood in the store with the Verizon employee, we watched as it drained very quickly while doing nothing. But they replaced it a couple days later with a brand new phone! Hooray!
Second Nexus - The 4G connection worked fine. The battery life was decent. My problem, however, was that 10-15 minutes into a call, the other person couldn't hear me. I could hear them clearly. This happened ALL the time. I got a replacement (a "pre-owned" btw). I then read about microphone cut-out problems on the internet and how they would be fixed with the upgrade.
Third Nexus - I had the exact same problems as the 2nd phone. I decided to wait for the software update because I'm a very patient person. I waited (and suffered) through a couple weeks of hanging up/re-dialing people all the time. The update came annnnnd........the phone still wasn't working right. Ok...so let's get another phone. The day the phone arrived, an employee at a non-corporate Verizon dealer told me about putting CyanogenMod on my phone and it would work great.
Fourth Nexus - I activated the 4th phone, and of course, it's like the first phone with battery, 4G, and microphone issues. Well, the 3rd phone was better than the 4th phone, so I considered keeping the 3rd phone and returned the 4th. I wanted to know, however, if putting CyanogenMod would violate my warranty, so I stopped in to talk to the Verizon corporate store employee before I sent the phone back. I also wanted to make sure with him that my phone was set up right. As I waited in the parking lot for 20 minutes for the store to open, I couldn't use my phone because I couldn't get a signal (IN A VERIZON STORE PARKING LOT). He said he didn't know about the warranty, but he said my phone was set up correctly.
Fifth Nexus - Have I mentioned I have been nothing but courteous and patient the entire time with everyone? I have. I absolutely have. Even the verizon store employees mentioned how calm and nice I was for someone who had been through so much hell. Thank you store employees. Thank you. Anyway, Nexus #5...ya know..that sort of sounds like a cologne... Nexus #5.... but it would most likely smell like Number Two...so let's pass. So anyway, Nexus #5 has the same problems as Nexus #1 and #4. I found a little section of the phone settings (under Battery>Cell Standby) that would tell you how much of the time you were without a signal. I didn't have a signal 28% of the time. In 6 hours the battery drained down to under 20%. In those 6 hours I received 6 texts and hit the Facebook button twice (I only got one page to come up and I closed it within 5 seconds). 80% of the battery was gone in 6 hours while I did virtually nothing on the phone.
So anyway, Verizon, while being very polite, has been absolutely worthless in their solution to my problem. They've offered me other phones which I didn't want. When you go into a store and pay $200 for a phone, you expect to get the phone you paid for. If you got home and found it was a different phone, would you not have a problem??? Around the 4th replacement, I mentioned giving me the Galaxy S3 instead. He said he couldn't because that's too new (and I completely understood). He offered the RazrMaxx (which was the only other phone I half-considered at the time of my purchase...but again..it's not what I wanted).
Well my 6th Nexus is on the way. And I'm sure it wont work. And I've spent 4 months in Verizon Nexus hell. And they'll probably have to send me Nexus #7. And I am willing to prove how each phone doesn't work from this point forward. I've asked them to remotely monitor my device if they could to see that I wasn't lying. I've offered to video the phone so they can see the batteries draining. I've taken these phones to corporate Verizon stores so they could witness the garbage phone I've been given.
So if this sounds like it's something you'd love to experience, then by all means, get yourself a Verizon Galaxy Nexus. If Verizon doesn't make it right VERY soon, I will absolutely be converting all my family members to a different service and recommending it to friends. I've already got the service picked out and priced 
