Update 2: Verizon has responded, and they disagree with many key points in the story here. Following is their full response:

The ZDNet story is inaccurate. This incident was reported to the authorities when we first learned of it months ago and an investigation was launched. Many of the details surrounding this incident are incorrect and exaggerated. No Verizon systems were breached, no root access was gained, and this incident impacted a fraction of the number of individuals being reported.

We take any and all attempts to violate consumer and customer privacy and security very seriously, so we notified individuals who could potentially have been impacted and took immediate steps to safeguard their information and privacy. Verizon has also notified law enforcement of this recent report as a follow-up to the original case.

This sounds pretty positive, and kudos to Verizon for reaching out on the Saturday before Christmas. The original text still follows for reference. 

Update: ZD Net has updated their original story, and it appears that the records are for FIOS customers and not wireless customers. We'll leave this in place so that the FIOS customers among you have a heads up

According to ZDNet, a hacker has gained access to over 3 million records from a Verizon Wireless customer database. The information includes names, addresses, serial numbers, and passwords. The hacker gained access to the server on July 12, and claims to have contacted Verizon, but since the have reportedly ignored his report, he has pasted 300,000 of the records online. Supposedly these database is broken up into regions, and the leaked region is in and around Pennsylvania. The records are stored in plain text, and the hacker "might leak the rest later".

If you're a Verizon customer, now would be a good time to change your account password. We're not going to go into the details or link to the pastebin of account data. We hate delivering this sort of news, but we know you need to be informed. We hope Verizon is quick to address the issue, and look forward to hearing their side of things. 

Source: ZD Net