Drupal 8 was officially released November 23, 2015.  

The Drupal community has a policy in place to maintain support for the 2 most recent versions of Drupal which, as of November 23rd, is Drupal 7 and 8. The community has extended support for Drupal 6 sites, but only through February 24, 2016. Obviously, with rare exception, 3 months is not enough time to transition platforms.  

What does this mean for Drupal 6 (D6) sites:

As of February 24th your site is no longer officially supported by the Drupal community. 

• The security team will no longer provide support or Security Advisories
• Bugs will no longer be resolved by the community

Current estimates put about 23% of Drupal sites on D6 [1]. With 113K sites still on D6 [2], patches will very likely be applied by D6 users for a while, despite the fact that the community has stopped officially supporting D6.

As more time goes by, fewer D6 sites will remain, thus making you more and more vulnerable. Your site might be fine for months, or even a year or two past EOL (end of life), but nothing is for certain.

Should I upgrade to D7 or D8?:

More than likely we recommend upgrading all the way to Drupal 8 unless:

• You plan to move very quickly on the project
• You have a complicated set of business rules 

By skipping Drupal 7, you are saving yourself the costs of having to move from D7 to D8 (which may be necessary in 4-6 years depending on how quickly D9 comes out). Even if you spend 20-30% more on a D8 site vs. a D7 site – it will pay off in the long run and save yourself tens of thousands of dollars.

The most important and commonly used modules have been included in Core for D8 (this is great news!!). If you have a lot of custom functionality – you’re likely better off with D7 since many custom modules have not yet moved to D8.

How important is it that I upgrade quickly?:

It depends. The main factor in this decision is your site’s current function.

Is your site a low-traffic, brochure style site? Is all traffic to your site anonymous?  If so, your site is fairly low risk. Even if it’s hacked, a good development team can replace it for you, and very little harm is done.

Is your site mission critical or does it collect personal data? How much would it cost you if your site was down for a few hours / days? Does your site require authenticated traffic and/or collect personal data?  If so, it's important to keep your site secure and up to date. We recommend that you upgrade as soon as possible. If a timely upgrade is not possible, talk with us about options to protect yourself such as, SSL certs, additional backups, and increased monitoring. You may also want to plan for additional support, just in case.

How long should I stay with Drupal 6?:

How long you stay with Drupal 6 is ultimately your decision. You’ll have to weigh the risks of staying vs. the reward of saving money on an upgrade (or even postponing an upgrade until it’s more convenient).

Feel free to contact Cool Blue with any questions or concerns and we will help make whatever transition you choose a smooth one. 

Source: https://www.drupal.org/drupal-6-eol 
[1]  http://w3techs.com/technologies/details/cm-drupal/all/all
[2] https://www.drupal.org/project/usage/drupal