How to log error to file, and not fail on exception

You could use the logging module:

import logging
logging.basicConfig(filename='/tmp/myapp.log', level=logging.DEBUG, 
                    format='%(asctime)s %(levelname)s %(name)s %(message)s')
logger=logging.getLogger(__name__)

try:
    1/0
except ZeroDivisionError as err:
    logger.error(err)

Running the script writes in /tmp/myapp.log:

% cat /tmp/myapp.log 
2010-08-01 17:50:45,960 ERROR __main__ integer division or modulo by zero

This will write your error to a log file and continue to run the code.

import traceback

#This line opens a log file
with open("log.txt", "w") as log:

    try:
        # some code
        # Below line will print any print to log file as well.
        print("Creating DB Connection", file = log)
    except Exception:
        traceback.print_exc(file=log)
        continue

As pointed out by Lott, if a download is failing, unless the problem is fixed upstream (or with your download address), the best you can do is to try again. However, if the situation is that you have a list of downloads, and simply want to skip over failed downloads instead of exiting, then:

logf = open("download.log", "w")
for download in download_list:
    try:
        # code to process download here
    except Exception as e:     # most generic exception you can catch
        logf.write("Failed to download {0}: {1}\n".format(str(download), str(e)))
        # optional: delete local version of failed download
    finally:
        # optional clean up code
        pass

Things to note:

(1) Use of the "logging" module, as suggested by ~unutbu, gives you much more flexibility and power with your logging output, including time stamp, simultaneously writing to different channels (e.g., stderr, file) depending on error levels, etc. etc.

(2) You might consider implementing the above logic using the "with" construct.