Log HTTP and HTTPS browser traffic, decrypting the latter

HTTPFox is a Firefox extension that will do the job.

===EDIT===

Right click the request panel and click "Copy all rows". Then you can save it to what ever editor you like - Openoffice spreadsheet for example. Please see the image that I provided.

HAR is HTTP Archive, and is exactly what you want to save (it includes HTTPS unencrypted).

Luckily this is now a basic feature of all major browser (it was not when you asked the question). No more need of third party extensions.

In Firefox (v41+):

• Start Firefox Developer Tools in Network mode (Top right menu > Developer > Network, or ctrl-shift-Q)
• Reproduce the target scenario
• Save the capture by right-clicking on the grid and choosing "Save all as HAR"
• Export the capture to a HAR file

Other browser:

In recent version of all browser, you can save HAR easily:

https://toolbox.googleapps.com/apps/har_analyzer/

Fiddler is definitely something you should consider even if it is not an extension but a separate application.