Inkscape

I used to do everything in GIMP. Filling objects in layers, creating outlines, it was all pixel-based.
But I just turned to Inkscape to do a little logo work for my mother, thinking logos should be scalable vector-graphics.
And OH MY GOD INKSCAPE I LOVE YOU
Expect me to be experimenting like Dr. Frankenstein with that program over spring break.

Additionally, other opensource programs I would recommend having:

LibreOffice (formerly OpenOffice): best Word-like program. In some cases, it surpasses its Microsoft rival. Plus, it’s free, but I’m never gonna advertise something you have to buy. The best things in life are free.
GIMP: Pretty standard Photoshop-quality program for image editing of any and every kind.
Audacity: Best audio recorder/editor out there. A bit of work, and you can get it to perform just like a regular mixing station.
Inkscape: If you’d rather work in vectors than pixels (or both is always good), definitely get this.
MuseScore: Not only is this as great of a music notation software as Sibelius, it can export any piece as an audio file, playing the notes with it’s MIDI soundboard. Useful if you want a driving synth-bass for your song but you don’t own a bass.
Hydrogen: A really (and I mean REALLY) nice drum machine. Only bug I find slightly annoying is that if you have this program running, it tends to monopolize your audio driver. I.E. no skype calls, no simultaneous MuseScoring. It’s probably something dumb that I haven’t figured out how to fix. I’ve only hit this recently, and still I’m already blown away.
Recuva: Now, I run Linux so this program isn’t really needed, but for you Windows people who tend to accidentally delete something important and it bypasses your trash and seems to disappear completely (whoops there goes that entire directory) or your computer crashes often and you don’t want to face the music and just switch to Linux, get this. Other important programs from Piriform are CCleaner and Defraggler.
Kdenlive: Face it: Windows video editing programs suck. Just dual-boot Linux already. This gem can be prone to crashing under the heavy weight of huge projects, but that just happens with any video editing software. Just save often and you’re golden. This guy is like Cinelerra only…well, different. But I like him.
KeePassX: Tired of remembering all those silly old passwords? Just keep them all in a secure and clever little program. Under a master password, you can not only store passwords, but there’s a neat little password generator that you can use to randomize all sorts of passwords that nobody would care to try and crack.