As far as I know, it varies from region to region within the US. Personally, as a resident of the northeast US, here are the terms I would recognize:
- seltzer is what I would normally call it, because when this is sold in stores (in my region), it's often labeled simply "seltzer". A Google image search for the term will turn up several examples (1, 2) of packaging displaying this label.
- sparkling water is used as a classy alternative to "seltzer", for example in fancy restaurants or by brands which want to give themselves a more refined image. Other answers/comments indicate that this is sometimes used for flavored water with carbonation, but I'm not personally familiar with that usage.
- club soda is another somewhat classy alternative, although not one that I hear very much. I believe it's the default in other parts of the US.
- seltzer water is recognizable but I would only expect to hear this from someone who isn't familiar with the word "seltzer" on its own.
- carbonated water is what I would use when talking to someone who is from a different region or different country if they don't recognize "seltzer".
- fizzy water is one I never hear used, but I would know what it meant.
I wouldn't recognize two cents plain or just sparkling. The former is an antiquated term according to Wikipedia. Also soda water is not something I hear very much and I'd probably figure it out after a few seconds of being confused.
I think most people are aware that the preferred term for plain carbonated water, as well as the meaning of several of these terms, varies from region to region, and so people are unlikely to find it strange if you use a term that is not the default in whatever region you're in. Technically there seems to be a difference between some of the various terms (e.g. source) but a lot of people are probably not familiar with those differences.
The variation in usage makes it difficult to find data on the relative frequency of using any of these words to mean one specific thing. For example Google Ngram may not be reliable because different people can mean different things when they say e.g. "sparkling water".