Visit http://sketchup.google.com/ to download SketchUp. If you are reluctant to provide the personal information they ask for on the SketchUp website, you can download it directly from here.
The download link for Pivot is here.
The download link for Pencil is here.
Blender is an excellent alternative to 3ds Max. Art of Illusion may also be an acceptable substitute (untested). It is available here.
Currently, there is no free alternative for Flash (that I know of), although Pencil does produce SWF files, which is the same format as Flash.
LibreCAD and Solid Edge 2D are two programs I have been asked to list here, but I haven't tested either of them for quality or AutoCAD compatibility.
Files can be backed up online in your Google Docs or your Dropbox (BDSS code) account.
Using the Dropbox link provided here will double the amount of space normally given when creating your account.
If you use Dropbox at school on your V: drive (which is public), you can keep it private by encrypting it with portable version of TrueCrypt. If you use Dropbox at school, always be sure your files are sync'd before you log out!
The download link for Portable Python is here. Be sure to download the 3.x version.
The download for the "original" Python is here. Be sure to get the 3.x version (whichever is offered).
See Turing Download for notes on where to get Turing.
GIMP is an excellent and free alternative to Photoshop.
Inkscape is an excellent alternative to CorelDRAW, Freehand, and Illustrator.
Picasa is excellent for minor editing and resizing of photos, for emailing photos to your contacts, or for uploading to Flickr or Facebook (plugin needed).
Greenshot is an excellent and free screen grabbing program.
HyperCam is a free screen recording program that captures both video and and audio from your microphone.
For recording podcasts, Audacity is free and excellent. You will also need the lame encoder to create MP3s.
PDF Creator is excellent for creating PDF (Acrobat) files. It installs like a printer, so you just print to it!
Bulk Rename Utility is excellent for bulk-renaming files such as pictures.
Print Free Graph Paper does not have to be downloaded, just run from the website. As the name indicates, it is used to print various types of graph paper.
Microsoft Security Essentials is an excellent, free anti-virus, anti-malware, anti-spyware program.
Lightworks is a professional-grade open source video editor.
KompoZer is an excellent and free alternative to Dreamweaver or Front Page.
Many of our assignments are created in Google Documents.
For offline word processing, Open Office and LibreOffice are compatible with many formats (including Word and Word Perfect) and are free.
Both Google Documents and Open Office can also be used for creating spreadsheets and drawings.
For more free software for home use, visit http://www.schoolforge.net/. If there's anything specific you think I should list, please let me know here.