Exit status set by comparison operator in bash script

$? is explained, though very briefly, in the Special Parameters parameters section of man bash:

   ?      Expands to the exit status of the most recently  executed  fore-
          ground pipeline.

@chepner put it best in his comment:

The key thing to understand is that each [ ... ] is a separate foreground pipeline, not part of the if statement's syntax, and they are executed in order, updating $? as you go along.

If you want to use an if-else chain, then save the value of $? in a variable, and use conditions on that variable:

wget -q "www.google.com/unknown.html"
x=$?
if [ $x -eq 0 ]
then
    echo "Fetch successful!"
elif [ $x -eq 8 ]
then
    echo "Server error response"
else
    echo "ERROR!"
fi

But in this example, a case would be more practical:

wget -q "www.google.com/unknown.html"
case $? in
    0)
        echo "Fetch successful!" ;;
    8)
        echo "Server error response" ;;
    *)
        echo "ERROR!"
esac