Must Have Free and Open Source Software

All of the applications are free to use, freeware or open-source. A couple of them have a trial period (you can still use the software after the trial has run out) or there's a purchasable version as well. I've also listed several similar applications (like Firefox and Chrome for browsers or Foxit Reader and Sumatra PDF for PDF readers) so that you can find your your own personal favorite. You don't need both, but it's nice to have something to chose from.

Video:

• VLC - Open source video player.
• Media Player Classic - Home Cinema - Light-weight media player for Windows. I personally like MPC-HC much better than VLC. Supports more codecs/formats and video looks better.
• Combined Community Codec Pack - A simple playback pack for Windows with the goal of supporting the majority of video formats in use today. Must have if you watch certain tv-shows or anime.

Audio:

• Foobar 2000 - Extremely lightweight and customizable free audio player for Windows. Supports a wide array of different audio formats.
• Audacity - Free, open source, cross-platform software for recording and editing sounds.
• Spotify - Listen to music for free.
• Grooveshark - Listen to music and radio stations for free.

Browsers:

• Firefox
• Chrome
• Waterfox - 64bit browser based upon the Mozilla Firefox source code.
• Pale Moon - Open Source, full-featured, speed optimized browser based on the popular Firefox browser.

Extensions for browsers:

• Reddit Enhancement Suite - Make surfing Reddit so much more enjoyable. Highly customizable and easy to set up.
• Adblock Plus - Blocks annoying ads on webpages and in videos. Surf faster and safer.
• Ghostery - Anti ad/tracking extension.
• ProxTube - Circumvent blocked Youtube videos.
• Speed Dial - Allows fast access to your most visited websites. Extremely useful if you visit or want to keep track off a lot of different websites.
• NoScript - Open source add-on (for Firefox) which allows JavaScript, Java, Flash and other plugins to be executed only by trusted web sites of your choice.
• ScriptNo - Similar to NoScript only for Chrome instead.
• Search by Image for Google (Firefox) - Fast way to reverse search an image. Very handy if you're looking for a source, more information or if anyone posts "original content".
• Search by Image for Google (Chrome)

Security:

• Microsoft Security Essentials - Lightweight antivirus software.
• Avast! Free Antivirus - Antivirus software.
• Malwarebytes - Anti-malware software.
• TrueCrypt - Free open-source disk encryption software for Windows 7/Vista/XP, Mac OS X, and Linux.
• Keepass - Free, open source, light-weight and easy-to-use password manager.
• LastPass - Another password manager that makes web browsing easier and more secure.

System, cleaning and recovery:

• CCleaner - A freeware system optimization, privacy and cleaning tool.
• Deffragler - Defragmentation software.
• Recuva - File recovery software.
• Speccy - Give you detailed statistics on every piece of hardware in your computer.

Communications:

• Skype - Call friends/family on their computers or phones.
• Pidgin - Open source chat client which is compatible with several different chat networks.
• Trillian - A fully featured, stand-alone chat client that supports several different chat networks.
• HexChat - IRC chat program for both Linux and Windows.

Documents, images and graphics:

• Foxit Reader - Free PDF reader.
• Sumatra PDF - Free PDF reader.
• Open Office - Open source personal productivity suite.
• Libre Office - Open source personal productivity suite for Windows, Mac and Linux.
• GIMP - Free image manipulation software.
• IrfanView - The best freeware image/graphic viewer for Windows. Extremely lightweight and supports a wide arrange of different formats.

Compression:

• WinRAR - File archiver (You can still use the software after the trial period has run out).
• 7-Zip - Open source file archiver.

File sharing:

• uTorrent 2.2.1 - uTorrent became extremely bloated after they released version 3.0 and on. Version 2.2.1 has everything you need without using many resources or having any ads.
• Transmission - Extremely lightweight BitTorrent client for Mac and Linux. There's an unofficial Windows version which you can get here: http://sourceforge.net/projects/trqtw/
• Deluge - Lightweight, cross-platform BitTorrent client.
• qBittorrent - Free, lightweight cross-platform BitTorrent client.

CD/DVD-tools:

• ImgBurn - Good, lightweight burning application.
• CDburnerXP - Another good, lightweight burning application.
• Virtual Clonedrive - Free media emulation software.
• DAEMON Tools Lite - Free media emulation software.
• PowerISO - Media emulation software.

Online Storage:

• Dropbox - Cloud storage.
• Google Drive - Google's cloud storage solution similar to Dropbox.
• Skydrive - Microsoft's cloud storage solution.

Other:

• Steam - PC-game client for PC, Mac and Linux (Linux version is still in closed beta).
• f.lux - Makes the color of your computer's display adapt to the time of day, warm at night and like sunlight during the day. Must have if you have problems with going to sleep or have problems with eyes or headaches.
• Open Broadcaster Software - Free and open source software for media streaming.
• Sublime Text 2 - A great text editor for code, markup and prose.
• Notepad++ - Free source code editor and Notepad replacement that supports several languages.
• Rainlendar - A lightweight customizable calendar.
• Hamachi - A hosted VPN service that lets you create LAN-like networks. Very useful if you want to play older pc-games with friends.
• Tunngle - A p2p VPN tool somewhat similar to Hamachi.