When you change jobs (I"ve recently started working for Google), you have to worry about health insurance.
In practice, it's not a big hassle. If you know nothing about it, you might think it'll be scary, but actually it usually works out just fine.
One worry is "pre-existing conditions". But most health "insurance" companies aren't allowed to - or just don't - block pre-existing conditions. At least, the new ones here don't.
Also, your old "insurance" company ... and your old employer ... typically have an arrangement whereby your health insurance doesn't end on, like, your last day of employment. (Things like life insurance might, but not health insurance.)
Rather, it ends on the last day of the month. So don't finish a job on the last day of the month, eh!?
(I write "insurance" in quotes because only a small part of it is actual "insurance" against catastrophic health situations. Most of it pays for routine maintenance, checkups and bureaucracy. So it goes.)