Most of these softwares are pretty well-known, but I want to give them some extra publicity. They are all free, but if you can afford it, I recommended taking a small percentage of the money you save on licensing (or irritation) and donating it to the developers.
Alternative to Microsoft Office: Open Office
Same functionality without jumping through proprietary hoops.
Alternative to Adobe Photoshop: GIMP
Most of Photoshop's functions, but you don't have to sell an organ to afford. Takes some getting used to for Adobe natives, but a couple hours' learning curve is still better than spending a grand.
Alternative to WinZip: 7zip
More options, lightweight, simple. No nag screens.
Alternative to Windows Media Player: VLC
No restrictions. Support for different formats. No spying.
Alternative to Adobe Soundbooth: Audacity
Easy-to-use audio editor.
Alternative to Internet Explorer: Firefox
More robust, optional add-ons that expand usability according to your specific needs.