scott, you are correct. Luckily I am currently gainfully employed, so not an issue for me right now. However, I have had to utilize COBRA in the past until benefits from the new employer kicked-in. I also had to administer COBRA to former employees because of my position at the company.
Good point about the 60-day window. The letter you speak of is important, too. I think it is called a "Letter of Insurability". It basically allows you to pick-up new coverage without the threat of a pre-existing condition. Without this letter, any pre-existing condition you have may not be covered by a new insurance company. For example, if you or your spouse are already pregnant when you sign-up for new insurance, and you don't have a letter of insurability, the mother's hospital and physician charges will be not covered. But, the baby's charges incurred upon birth will be covered as they would be considered a new dependent after the coverage begins. This is, of course, only applicable for family, not individual, coverage.
COBRA not only allows you to pay for continuing coverage once you leave a job, it also protects you from pre-existing condition clauses as long as the rules are followed.