COBRA stands for The Consolidated Omnibus Budget Reconciliation Act (of 1986). COBRA is a continuation of benefits from your employer. It contains provisions giving certain former employees, retirees, spouses and dependent children the right to temporary continuation of health coverage at group rates. It is usually significantly more expensive than what you've been used to paying because your employer might have been paying part of, or all of the premium.

When you should absolutely take COBRA

You have had recent health problems.
You have ongoing health problems.
You or your spouse is currently pregnant.
You are taking expensive prescription medication.
You are in danger of exceeding the COBRA enrollment period.

When should you opt for an individual plan instead?

If none of the above circumstances applies to you, we recommend applying for individual coverage immediately.  First of all, COBRA is a temporary solution.  Sooner or later your COBRA coverage will end.  You absolutely do not want to be in a position where you could incur an expensive medical circumstance, while holding temporary coverage.
Secondly, COBRA is expensive.  You will likely experience significant savings by utilizing individual coverage options.  Finally, your COBRA coverage is still controlled by your former employer.  If your previous employer changes their group coverage, your plan will change as well.