Oddly enough, "plastic" is less universal than it seems to be. For example, I cannot use my European credit card at many US gas station pumps (where you usually swipe the card at the pump): In parts of the US it works, in other areas I have to enter a five digit ZIP code, except that my German post code is not recognized or accepted. So I have to go inside, at which point I might as well use cash. Similarly, one of my (German) cards includes a PayPass function, but I cannot get it to work in the US. (Have not done extensive research regarding PayPass though.

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On the other hand, Americans who travel to Europe sometimes run into problems because many of their credit cards have a magnetic stripe only, but no chip. So machines in Europe that read the chip are likely to refuse those American cards.
As for checks, I have not used one in ages. Cell phone payments, well, I use them for the subway in my home city for example (not being a regular user), and there are services such as mpass.de ... except they are not widely used, mostly for web site payments. Also, from a euro user's point of view, many of these services are limited to payments in one country only. The € cash is a little more advanced in that regard.

Christian