The proper answer would be: "it depends"
You do want in general log the exceptions that you catch, since they correspond to something going wrong. That is why code analysis tools such as sonar will raise warnings when you do not log them.
Consider the following taks: parsing a file. While parsing the file you actually try to parse each line. Sometimes some lines will be malformed, and therefore you don't want to stop parsing the file because of it. In that case, you probably want to just log the wrong line and keep going on the file.
However, imagine that at some point you encounter an I/O exception while reading (for example some other program deleted the file while yours was accessing it).
In this case, you will probably want to log your log the error you encounter, and throw a new exception to stop processing the whole file.
So in short, you have to think about what is the best thing to do. But both practices are not bad.