For many people looking to keep health insurance after losing their job they first look at COBRA coverage offered by their employer. For many job seekers this just affordable (especially for people who were laid off well before the Obama Stimulus Package allows for COBRA subsidies.)
For myself, I've been using Assurant Health for my health insurance provider while I'm looking for work. So far I've been pleased, and recently I signed up for their affiliate marketing program---so this post is a little bit of an advertisement.
It never hurts to cross-shop and get quotes to see if COBRA has the best deal or some other insurance company does---so for a peace-of-mind, consider getting a quote from Assurant for your health insurance needs.