The Two Cents column on emergency funds has the good, standard advice offered by financial planners and investors.
There's a 1-3-6 guideline for deciding how much to save, with a link on the page to a different article offering a 3-6-9 guideline.
Of course, this assumes you have enough money to squirrel away to being with. Most of my adult life was spent at interesting but lower-paying jobs and paying off credit card debt racked up during periods of unemployment. If I had enough cash to contribute to my 401K and cover my bills, anything extra went to paying off the credit card.
It is only fairly recently that I reached a certain comfort level with how much I have in the bank, but I will always feel I started too late and saved too little.
The YNAB blog has its own take on do you really need an emergency fund. YNAB, an online budgeting application, stands for "You Need a Budget"; I started using it about 1.5 years ago and wish I'd known about it years earlier. It changed my financial life (but that's a story for another blog post).
I thought the YNAB article more applicable to my situation than the Two Cents piece. As the YNAB writer notes, and I've seen in my own finances, the more I'm tuned in to my priorities and budget categories, the less need I have of a line item for emergencies.
If an emergency car repair or dermatology visit results in a surprise bill in the hundreds of dollars, I now have enough saved in those categories to cover the expense. So emergencies are covered by my "true expenses" categories, where expenses are variable, hard to predict, but tend to be outsized.
Having enough money to cover an unexpected expense is a good feeling, one I've not had for most of my adult life, and I savor it.