How do I can format exception stacktraces in Python logging?

You can define your own Formatter whose methods you can override to format exception information exactly how you want it. Here is a simplistic (but working) example:

import logging

class OneLineExceptionFormatter(logging.Formatter):
    def formatException(self, exc_info):
        result = super(OneLineExceptionFormatter, self).formatException(exc_info)
        return repr(result) # or format into one line however you want to

    def format(self, record):
        s = super(OneLineExceptionFormatter, self).format(record)
        if record.exc_text:
            s = s.replace('\n', '') + '|'
        return s

fh = logging.FileHandler('output.txt', 'w')
f = OneLineExceptionFormatter('%(asctime)s|%(levelname)s|%(message)s|', '%m/%d/%Y %I:%M:%S %p')
fh.setFormatter(f)
root = logging.getLogger()
root.setLevel(logging.DEBUG)
root.addHandler(fh)
logging.info('Sample message')

try:
    x = 1 / 0
except ZeroDivisionError as e:
    logging.exception('ZeroDivisionError: {0}'.format(e))

This produces just two lines:

01/28/2015 07:28:27 AM|INFO|Sample message|
01/28/2015 07:28:27 AM|ERROR|ZeroDivisionError: integer division or modulo by zero|'Traceback (most recent call last):\n  File "logtest2.py", line 23, in <module>\n    x = 1 / 0\nZeroDivisionError: integer division or modulo by zero'|

Of course, you can build on this example to do precisely what you want, e.g. via the traceback module.

For my usecase Vinay Sajip's code did not work good enough (I worked with more complex message format), so I came up with this one (for me it's also cleaner):

class OneLineExceptionFormatter(logging.Formatter):
    def format(self, record):
        if record.exc_info:
            # Replace record.msg with the string representation of the message
            # use repr() to prevent printing it to multiple lines
            record.msg = repr(super().formatException(record.exc_info))
            record.exc_info = None
            record.exc_text = None
        result = super().format(record)
        return result

So this format() method can detect that an exception is going to be logged and can just convert it to its string representation and formatting of the log message happen simply for that plain message string. I tested it in python 3.