Last week I finally sat down and started working on a logo for Noadi's Art. This led me to do a lot of searching online for tutorials and software. Here's some of the good ones.
I love open source software, partly because it's free and also because most of it is cross platform and can run on many operating systems.
I really recommend using a vector software to create the logo because it makes scaling the logo up or down very easy and without loss of quality.
Inkscape - Vector image software. Not quite as powerful as Adobe Illustrator but still very good and with all the most common tools.
The GIMP - Powerful image editing tool comparable to Photoshop
Step-by-Step Logo - I don't know about you but I love to see examples of how other designers work—they reveal better (or worse) ways of doing things and allow me to gauge whether my methods are mainstream or totally whacked-out.
Logo Design Process Tutorial - One of the main aspects of the branding process includes logo development.
Graphic Design 101 - Lots of resources covering graphic design
The Basics of Graphic Design - This tutorial examines the process of graphic design for printed publications, presentations, and web sites.
Many logos include text so you need a good font. There are loads of good free or inexpensive fonts available online, here are a few good sources.
Blambot Comic Fonts and Lettering - These are some very fun fonts which are good if you want something inspired by comics, pulp covers, or science fiction/horror films.
dafont.com - Large collection of free fonts of varying quality
40+ Free Fonts for Professional Design