Formal undergraduate design education traditionally offers these things:
A) technical skills
B) contextual knowledge
C) social learning, critique
D) networking opportunities
E) recognised credential
I have met many successful designers who haven't got a degree in graphic design and who I, with now 5 years of academic study under my belt, look up to. I don't believe that they were born with the knowledge and talent that I admire about them, instead I'm convinced that with the right attitude anyone can acquire a design education without attending a formal design programme at a university.
A) Like at design school, you need to practice your technical skills in order to become proficient in using the tools of your trade. Good starting points are the various tutorial sites that explain step by step how to use a software, tool or technique. Even the help pages of Adobe's Creative Suite can be a great technical self-education tool.
B) Read, read, read. It's what you normally do at university too. Depending on what area of graphic design you're interested in, find books on typography, layout, user experience, semiotics, anything. They don't have to be picture books either. I could make tons of recommendations, but if I had to pick one Universal Principles of Design by Lidwell et al. is great. But not only books are great resources for relevant contextual knowledge. There's a great number of very relevant design blogs, not just those that post 50 roundup posts with 300 random images every day. Find design blogs that stimulate your thinking, not just inspire you visually.
C) The social wrapper traditionally provided by universities is probably the most important aspect that people would mention when it comes to choosing to go the university path or not. In reality the quality of this social experience varies greatly depending on the programme you're in, the number of students, the student to lecturer ratio, the background of students and lecturers etc. In graphic design we're lucky enough that these days our practice has largely shifted to the digital domain. Social media enables you to actively (conversation) and passively (follow) engage not only with great designers and role models but also with peers that are on the same level as yourself. Put your work and your questions out there through social media channels like twitter, facebook, dribbble, flickr, YouTube ... you name it. Of course some feedback and responses can be trivial, but that's the same at university! If you want to get your work critiqued, be proactive, start the conversation and ask questions (you're already doing that here). Don't restrict yourself to the online medium though. Find friends or other designers who can feedback on your work. Be aware that you're your own teacher, nobody's going to tell you what's right and what's wrong. Find an internship, voluntary work, take part in competitions. These are all opportunities for critique. It doesn't always have to be a renowned design legend and in most courses you don't get this anyway.
D) following on from the last point, make the most of your social network to get freelance work, work opportunities, clients, advice etc. There are many free design related lectures everywhere, go to them, talk to people, network. Network with people on twitter, collaborate on projects. Networking is something the web excels at, you don't need to study graphic design at university for that anymore.
E) The degree is probably the only thing you can't get through all the free resources out there. It's the only thing you actually pay for at university. On the other hand a degree isn't required to be a graphic designer. I hope the industry will soon notice that too.