How do I determine if a web page exists with shell scripting?

Use cURL to obtain the status code and check for required values.

status=$(curl -s --head -w %{http_code} http://www.google.com/ -o /dev/null)
echo $status

Under a *NIX, you can use curl to issue a simple HEAD request (HEAD only asks for the headers, not the page body):

curl --head http://myurl/

Then you can take only the first line, which contains the HTTP status code (200 OK, 404 Not Found, etc.):

curl -s --head http://myurl/ | head -n 1

And then check if you got a decent response (status code is 200 or 3**):

curl -s --head http://myurl/ | head -n 1 | grep "HTTP/1.[01] [23].."

This will output the first line if the status code is okay, or nothing if it isn't. You can also pipe that to /dev/null to get no output, and use $? to determine if it worked or no:

curl -s --head http://myurl/ | head -n 1 | grep "HTTP/1.[01] [23].." > /dev/null
# on success (page exists), $? will be 0; on failure (page does not exist or
# is unreachable), $? will be 1

EDIT -s simply tells curl to not show a "progress bar".