How can I see the entire HTTP request that’s being sent by my Python application?

A simple method: enable logging in recent versions of Requests (1.x and higher.)

Requests uses the http.client and logging module configuration to control logging verbosity, as described here.

Demonstration

Code excerpted from the linked documentation:

import requests
import logging

# These two lines enable debugging at httplib level (requests->urllib3->http.client)
# You will see the REQUEST, including HEADERS and DATA, and RESPONSE with HEADERS but without DATA.
# The only thing missing will be the response.body which is not logged.
try:
    import http.client as http_client
except ImportError:
    # Python 2
    import httplib as http_client
http_client.HTTPConnection.debuglevel = 1

# You must initialize logging, otherwise you'll not see debug output.
logging.basicConfig()
logging.getLogger().setLevel(logging.DEBUG)
requests_log = logging.getLogger("requests.packages.urllib3")
requests_log.setLevel(logging.DEBUG)
requests_log.propagate = True

requests.get('https://httpbin.org/headers')

Example Output

$ python requests-logging.py 
INFO:requests.packages.urllib3.connectionpool:Starting new HTTPS connection (1): httpbin.org
send: 'GET /headers HTTP/1.1\r\nHost: httpbin.org\r\nAccept-Encoding: gzip, deflate, compress\r\nAccept: */*\r\nUser-Agent: python-requests/1.2.0 CPython/2.7.3 Linux/3.2.0-48-generic\r\n\r\n'
reply: 'HTTP/1.1 200 OK\r\n'
header: Content-Type: application/json
header: Date: Sat, 29 Jun 2013 11:19:34 GMT
header: Server: gunicorn/0.17.4
header: Content-Length: 226
header: Connection: keep-alive
DEBUG:requests.packages.urllib3.connectionpool:"GET /headers HTTP/1.1" 200 226