Blender is a complex piece of software that is capable of producing extremely high-quality visuals for all manner of visual art purposes, from video games to product visualization. Of course, that power needs to be wielded by a controlled hand. Otherwise, you'll end up with a mush of digital geometry that makes no sense at all.
These days, video tutorials are the educational tool of choice for most people. I'm going to give you five of the best free beginner video tutorials for Blender currently available. I recommend you watch all of them. They all cover a lot of the same information. However, every instructor has a different way of presenting. Stick with the one that clicks with you.
(Full disclosure: I moderate a forum that's currently maintained by CG Cookie.)
CG Cookie's Blender Basics series of tutorials is the first place I send most people when they want to start familiarizing themselves with Blender. I like the teaching style they use here. You get a quick overview of Blender and its interface. This series is often enough to get a person reasonably comfortable with the way Blender works, and it serves as a nice reference to look back if you ever find yourself getting lost.
The Blender Foundation has an excellent YouTube channel. Not only can you see talks from previous Blender Conferences and completed Open Movie projects, there's also a great Blender First Steps playlist. You might consider this to be the "officially sanctioned" beginner tutorial series on Blender. There are 41 videos in this series, but they're all pretty short and get right to the point. This might be your best quick-reference option.
If you're already familiar with the basic concepts of 3D graphics from another suite but you're new to Blender's way of doing things, I'd recommend the Blender Inside Out series available on the Blender Cloud. These are a great set of videos that can help anyone migrate from one of those other proprietary tools more smoothly.
It's my opinion that the folks over at CG Masters don't get enough love for the video tutorials they produce. As an example, they have a nice Blender Beginner series that does quite a nice job of getting you through the very first stages of Blender, including the installation process and a brief overview of the interface. If you need to start at the absolute beginning, this is probably where I'd point you to first.
And, of course, any list of Blender tutorials would be incomplete without mentioning the fine tutorials over at Blender Guru. The Blender Beginner set is really nice and takes a more project-based approach than a lot of the other tutorial series. This is the infamous "donut" tutorial series. Its nine parts start with a brief survey of the interface, then get right into the process of making a 3D model, texturing it, lighting it, and rendering it to an image you can share with folks.
That's the rundown! Five very fantastic tutorial series that are sure to get you up and running with Blender so you can make your own very cool things in 3D. Did I miss any? What's your favorite Blender tutorial series?