Text is not wrapping

interestingly, you are using   ‘non-breaking-space’ characters in your test content; on purpose or by mistake (?)

example: Testing Testing Testing Testing Testing 

and these are doing what they are meant to do – i.e. not breaking.

try and use a ‘normal’ sample content to test themes, such as ‘lorem ipsum’.

I’m basically typing it directly into the WordPress visual editor. Not importing it, just typing it directly into the app.

While something like word-wrap: break-word; could momentarily fix your problem, it’s not anywhere near an ideal solution.

When using the visual editor, do you have it set to Visual or HTML? When live editing the code of your site and adding in some filler text in place of the Testing, I see that it is breaking properly. As alchymyth has pointed out above, you are using   in your text. As the name implies, it is non-breaking, meaning it will continue to go until a break is found.

You mentioned that it happens with each theme that you tried, so my guess is just in how you copied and pasted the testing in. I see on other posts that other text properly breaks.

did the problem start after an update?
or is this a new install?

seems to be caused by the editor tinyMCE; however, unfortunately, I have no idea what causes it and how to solve it.

related:
https://wordpress.stackexchange.com/questions/29702/wordpress-automatically-adding-nbsp

in extreme, consider to re-install the full WordPress installation.

Went in, deleted the first test post, created a ‘test2’ post. In this one, used the option of pasting as text. That seems to work. But sort of odd that I can’t type it directly into the tool, isn’t it?

New installation. In fact, I’ve already uninstalled and reinstalled it once. Problem remains.