Almost everyone I’ve seen using them on the web (myself included) does that. Very few people I’ve seen set them open.

(Lots of people use en-dashes set open instead of em-dashes set closed for the uses for which they are interchangeable as a matter of stylistic preference, though.)

I believe this is specific to the US. Writing from other English-speaking countries often uses an en dash surrounded by spaces instead of an em dash.

I didn't know that was the correct way to use them. It feels incorrect in a space delimited language. Interesting.