will be traveling to Czech Republic, Germany, Austria, and Hungary (in that order) for about 12 days.... is there a SIM card that works for all those countries?

Do you have an Android phone? Check with your carrier your smartphone may work without a SIM card.

sure, the phone will work as a minicomputer as long as you have access to Wifi, but you can't text or make phone calls that way, which I presume is what the OP wants to do. And sure you can use its radio or listen to music. But it won't be a phone.

Now you can use Google Whatsapp for texts and get some apps to use Wifi for phonecalls, if you know about those things and want to.

Legally all EU country networks must work in all the others, so the real issue is what will you find at your first airport stop in Europe. Plus of course you need to know what services you require. I think Vodafone is at Prague, or you could order for local delivery.

Thank you for your reply. Good to know EU has that agreement. Cheers

Not only must the SIM work in all EU countries but you cannot be charged roaming fees. You will still be charged a lot if you buy your SIM in Czechia and use it to phone Germany or wherever whilst still in Czechia. However once you are in Germany or wherever your call to another country will be at local rates.
Look at Vodafone. make sure you load enough onto the card for the duration of your trip as it is not always possible to load more money onto it when traveling, especially with a foreign credit card. Vodafone NL allow it, but that doesn't mean they allow it in other countries.
Make sure your phone is unlocked before you leave home or a new SIM won't work!

I recommend the Dutch Vodafone SIM. I bought one on eBay last year and then used it in Slovenia, France, and Italy...and this year I used it in Spain and Portugal. (Never used it in the Netherlands yet!) Search eBay for "vodafone you nl" and find the one for $5 + shipping (seller "eurosims"). The SIM comes with no credit on it - you have to add that later. I created an account on the Dutch Vodafone website while in the US with this SIM (free incoming texts). Vodafone is not the same company (technically) between countries, so you have to use the Dutch site. I use Google Chrome which can translate Dutch automatically. I added credit to the SIM in my new Dutch Vodafone account using my US credit card. They have online chat for support (in English if need be) - haven't used it but others who have say they have been very helpful.

Don't add credit to the SIM until soon before you will depart for Europe - it's good for only six months (but gets extended each time you make a transaction). You buy "you" bundles with the credit you add to the SIM - currently 2GB for 10 euros, 6GB for 20 euros - each good for 30 days from the time you activate it, so don't activate a "you" bundle until you need it.

Andrew thank you for your answer.
I will be travelling for 3 weeks: Ukraine (Lviv and Kiev) and Prague. I have iPhone. What is your advise for me?
I was in Portugal last year/ I bough SIM card in Lisbon in airport.

I would probably do the same thing in Ukraine: buy a SIM at the airport (or train station) when you first arrive. Unfortunately, EU roaming doesn't help you in Ukraine. You can buy another SIM when you get to Czech Republic.

If you live in the US, Sprint and T-Mobile customers would get free 2G data and free texts (and 25 cents/minute calls) in both Ukraine and Czech Republic. Verizon and AT&T both have day pass and monthly pass options for international roaming that cost more.