As a resident in Germany, you must have (by law!) a health insurance, even if unemployed. With this insurance comes a European Health Insurance Card (EHIC), that grants you insurance in any European country plus a few (Iceland, Liechtenstein, Norway, Switzerland and the United Kingdom) "under the same conditions and at the same cost (free in some countries) as people insured in that country" (source).
But what happens when traveling outside Europe?
You're basically on your own, and it very much depends on the country you're in. Some will charge crazy amounts for any treatment or care (hello USA!), some are cheap. Also, what if you need repatriation?
Because you want to travel stress-free, I recommend taking out a private health insurance for trips abroad. For example, I am insured with TK and they offer two options, depending on how long the trips are. For trips under 60 days, the options are:
TravelPlus (TravelXN), via Envivas
It's a yearly subscription of 11.9 euros that you pay until you cancel it (you can cancel this anytime). And you're covered!
TK-Tarif Traveller, also via Envivas
It's a free contract (no charges), and it stops being free the day you need treatment abroad (but you won't pay more than 24 euros per year). It's a 3-year contract, that cannot be terminated earlier. Also, it's considered as an optional deductible tariff, meaning TK will let the Finanzamt (tax office) know that you signed up for this. The value of this "monetary benefit" is 11.90, and you'll have to state this in your Steuererklärung (tax declaration) and probably pay some tax off it every year (a couple of euros).
Der TK-Tarif Traveller ist ein Selbstbehalt-Wahltarif und enthält als Prämie eine private Auslandsreise-Krankenversicherung der Envivas Krankenversicherung AG für unbegrenzt viele Privat- und Geschäftsreisen bis zu einer Dauer von 60 Tagen. [...] Die Techniker ist gesetzlich verpflichtet, den geldwerten Vorteil des Reiseschutzes von jährlich 11,90 Euro zur Versteuerung an die Finanzbehörden zu melden.
Conclusion
I would recommend the first option, as it's very cheap, you can terminate the contract anytime, and it has nothing to do with your Steuererklärung. I would also only recommend taking out a private health insurance for trips abroad depending on your destination, how far from home it is, how expensive treatements in this country are... For the USA for instance, it's a no brainer, totally worth taking this out.