Free Utilities

I've categorised most of these by platform compatibility, and whether they're Open Source Software (OSS). Hope you find something useful!

Download Managers

wxDownload Fast (OSS, Win/Mac/Linux)
Multithreaded, multiplatform and free.
Free Download Manager (OSS, Win/Mac)
Haven't tried it myself, but had it recommended.

FTP Clients

FileZilla (OSS, Win/Mac/Linux)
A nice open-source FTP client (and server, but I haven't tried that) for Windows. Pretty quick and easy to use once you set it up correctly.

Log Analysers

AWStats (OSS, multiplatform)
A free web/mail log analyser with extensive reporting.
Analog (OSS, Win/Linux/etc)
A webserver logfile analyser. Takes a lot of configuration, but is very customisable, producing useful graphs and tables.

Miscellaneous Utilities

AnalogX Utilities (Win)
OK, so this should really be in the 'links' section there's so much useful stuff on this site. This is one excellent programmer - most utilities come with installers/uninstallers in one file that totals 250k or so! Surf around, there's sure to be something useful there.

Mail

Thunderbird (OSS, Win/Mac/Linux)
A great open source email client.

PDF Viewers

Foxit Reader (Win)
A much lighter weight alternative to Adobe Reader
SumatraPDF (OSS, Win)
An open source Windows reader. For more OSS readers and other platforms, see PDF Readers.

Proxy Servers & Web Filters

uBlock Origin (Firefox, Chrome)
The most performant ad-blocker for browsers.
Adblock Plus (Firefox extension)
An alternative ad blocker I used to use.
Privoxy (Win)
A local HTTP proxy that can enhance the surfing experience.

Security

PuTTY (OSS, Win)
A great open source SSH client for Windows.
VeraCrypt (OSS, Win/Mac/Linux)
Free disk encryption software.

Windows Tweakers

System Internals (OSS, Win)
Again, technically a link but I had to include it here. This is a site full of small monitors that allow you to watch the innards of Windows at work. For instance, there are programs to monitor all accesses to disks and the Registry, as well as programs to show DLL dependencies and lists of open files and ports. If you understood all that, you need these.
Resource Hacker
This is a program to extract resources, such as pictures, icons, cursors, sounds and even entire menus and windows out of programs. It can also modify those resources, with its own internal resource compiler and decompiler, meaning you can rearrange dialogs, menus, pictures and so on within your favourite programs. For instance, I once replaced the picture up the side of the Start Menu and rearranged Winamp's context menu to suit my taste. This is an awesome piece of code, and an essential download for the advanced user who really likes to tweak.

Zip Utilities

7-Zip (OSS, Win)
Reputed to have extremely good compression levels, especially with its own archive format. A small download, too.

Disk / File Recovery

TestDisk / PhotoRec (OSS, Linux, Mac, Win)
Open source disk recovery and file undeletion software, console interface.

Tell Me More

I'm always willing to hear of any interesting new downloads!