Mozilla Firefox 52.0 32-64 bit Multilingual

Web browser without installation.
Portable Nightly MultiVersion 32-64 bit en-US Online (0.4 MB) 10/11/15
In first screen enter Version Number: 55.0a1
Portable Aurora MultiVersion 32-64 bit Multilingual Online (0.5 MB) 24/03/15
Select language and enter Version Number: 54.0a2
Portable Firefox MultiVersion 32-64 bit Multilingual Online (0.5 MB) 23/03/15
Select language and enter Version Number: 52.0 or 52.0esr or 45.8.0esr
Portable Firefox MultiVersion Multilingual Online (0.4 MB) 28/04/14
Select language and enter Version Number:38.8.0esr

Final and Beta use same launcher and profile but Aurora and Nightly have their own.

64-bit variant of Firefox without installation.
Download Portable Waterfox en-US Online (0.4 MB) 07/01/16
In first screen enter: 51.0.1
Can use Java Runtime Environment Portable

Optimized Firefox Browser without installation.
Portable Pale Moon 27.x 32-64 bit Multilingual Online (0.5 MB) 06/01/17
Select language and enter Version Numberr: 27.1.2
Portable Pale Moon 26.x 32-64 bit Multilingual Online (0.5 MB) 26/01/16
Select language and enter Version Number: 26.5.0
For Windows XP download palemoon-24.7.2.win32.installer.exe and (if needed) palemoon-24.7.2.win64.installer.exe and run Pale_Moon_Portable_24.7.2_32-64_bit_Multilingual-Setup_Extractor.exe in same folder.
On first run, check allow Language Pack installation, click on Continue but close and restart by launcher.

PasswordFox for Firefox Portable.
Download PasswordFox 1.57 Multilingual Online (0.5 MB) 31/01/17
Extract and run PasswordFoxPortable.

NPAPI Flash Plugins

Multilingual Online will download setup in selected language (Afrikaans, Shqip, عربي, Հայերեն, অসমীয়া, Euskara, Беларуская, বাংলা (বাংলাদেশ), Bosanski, Brezhoneg, Български, Català, 中文 (简体), 正體中文 (繁體), Hrvatski, Čeština, Dansk, Nederlands, English (British), English (South African), English (US), Esperanto, Eesti keel, suomi, Français, Frysk, Pulaar-Fulfulde, Gàidhlig, Galego, Deutsch, Ελληνικά, ગુજરાતી, עברית, हिन्दी (भारत), magyar, íslenska, Bahasa Indonesia, Gaeilge, Italiano, 日本語, ಕನ್ನಡ, Қазақ, ខ្មែរ, 한국어, Latviešu, lietuvių kalba, Македонски, മലയാളം, मराठी, Norsk bokmål, Norsk nynorsk, ଓଡ଼ିଆ, فارسی, Polski, Português (do Brasil), Português (Europeu), ਪੰਜਾਬੀ, română, Русский, Српски, slovenčina, Slovenščina, Español (de Argentina), Español (de Chile), Español (de México), Español (de España), Svenska, தமிழ், తెలుగు, ไทย, Türkçe, Українська, Tiếng Việt, Cymraeg, isiZulu) and extract files.

Settings of installed Firefox should be preserved.
Multi-Users: change Profile by editing FirefoxPortable.ini or PaleMoonPortable.ini with User=NameOfNewUser.