Most of the time, it's not necessary to buy expensive software. I'm always hunting for freeware and here are some interesting programs, which I had found over the years.

Image Editing

Pixia
Japanese painting software.
field of application: Illustrations, Image Editing

Image Tricks
Is an application only for Mac Users.
There is a free and a pro edition.
field of application: image editing and generating

The Gimp
I think, this is the most powerful freeware image editor.
field of application: image editing
If you want a more photoshop like look, try Gimp Shop

paint.net
field of application: image editing

Magix Photo Designer 7
field of application: image editing

Painting Programs

Project Dogwaffle
I compare this application with Fireworks.
field of application: paintings, animations

Microsoft Expression
Sorry, but it's a german download site (I didn't find an english download site). This a vector program with different brushes. You can combine it with your own bitmaps. It's a beta version, but I used it, as I started as a freelancer with no money. :-)
And this is the download site I trust the most. I always download software from there.
field of application: vector paintings

Inkscape
Powerfull Open-Source Editor.
field of application: vector paintings

Artweaver
field of application: painting program

Ultimate Paint
field of application: painting, creating and manipulating images

Photoshop Filters and stand-alone Filters

Virtual Photographer
I prefer this filters for dramatic landscapes. It's a photoshop Filter, but you can download the Virtual Studio as a stand-alone.

Dreamy Photo
You can create romantic portraits with it. The installation puts the plugin into your photoshop filter folder, but you can use it also as a stand-alone filter without photoshop.

Another freeware plugin from Auto FX is Mosaic

Xero-Graphics
Xero-Graphics has a ton of freeware filters.

Cybia
Has some freeware photoshop filters which are simulating effects of the non-digital area.

Ulead
Filters for creating backgrounds and abstract pictures.

FilterForge Freepacks
There are 6 Filterpacks for free at the moment.

Little Ink Pot offers 3 freeware filters which are very usefull to simulate illustrations.

Redfield offers several free Plugins. I love the Lattice Composer.

Red Paw Media has some interesting free filters like BleachBypass.

The Plugin Site offers a pack of free Plugins for channel converting and simulating red/green color blindness. Which is very usefull for information graphics.

VanDerLee has some plugins for simulating snow (and more).

Flaming Pear has a pack of free plugins. Just scroll a little bit down on the website.

Image Converting

RawTherapee
Very helpful, when your photoshop version is too old for a newer RAW Plugin.

JPG-Illuminator
Unfortunately the site is in german without translations. It's a programm especially for white balance, color timing and brightening.
A large german Forum for Digital Photography is supporting this program with tutorials.

Desktop Publishing

Scribus
It's not necessary to buy expensive Suites for some Flyers or business cards. I used this program when I startet my self-employment. I made my first layouts with it without any problems.
You need the Postscript and PDF interpreter/renderer Ghost Script

Resources

DaFont
Huge amount of freeware fonts but you must keep a close watch to the different licences.

Wiki Commons
The same here. Pictures for free use, but pay attention to the licences.

FlickR has thousands of pictures under several Creative Commons Licences.