My personal favorite graphic design related website. There's plenty of professional designers who post on there, and it gives a better idea of what the field is like than anything else I've found. As with any forum, it takes some getting use to the "culture" but there is virtually unlimited information to be found here.
Some areas of interest within this forum:
This is the area where work is posted for critique. The critique can be pretty brutally honest at times (hence the "wear your heavy sweater!") but it is generally constructive criticism. Most of the stuff posted is by newer designers, so you can learn a lot just by reading over peoples' feedback and identifying common themes. Before you can make a good design, you have to recognize it!
Isiah pretty much covered this in his What Makes a Good Logo? post, but I figured I'd throw this up as well. It deals with a lot of the same concepts.
It's exactly what it sounds like. There's a ton of information here. Have fun!
This isn't as much as the process as it is the profession. For anyone looking at graphic design as a profession, this is a good place to get an idea what the ups and downs of it are.
This is a blog dedicated specifically to web design. It typically has a solid mix of tips, resources, and showcased designs. Since some of it deals with the coding side of web design, not all of it is applicable to graphics. Nonetheless, it has quality content. Perhaps it will even pique your interest in web design.
Typography is essential to good graphic design. I Love Typography is a blog devoted entirely to it, and it's much more interesting than you might expect. In particular, check out this introductory post. It, along with part two, contain the basics of typography.
Here's some nice sites to check out if you're stuck on a design, or just feel like browsing.
Resource suggestions in the comments are welcome!