I want to ditto what the others said about
not having a gap in coverage...in general, for most decent companies having decent insurance. However, there are insurances that are so bad that they never cover pre-existing conditions, ever. In that case, federal law allows you to COBRA your old insurance--even if you have new insurance--if that new insurance happens to have pre-existing condition exclusions. When I moved to Texas for a new job (after having been unemployed for five months) I discovered my company had just such an insurance plan, so I continued to COBRA my old insurance until I found a better job. Expensive, true, but it was worth it. My advice is that for most insurances all you need to do is avoid that gap in coverage, but definitely check up on the details of your new insurance before you sign anything. Also, beware of waiting periods when you start employment--some companies will have a period where you are ineligible for benefits at the start of employment, and you may want to COBRA your current insurance then, too.