Some really great and free Unity3D tutorials are available at Walker Boys Studio in the form of videos on Vimeo with support files for download.
Chad and Eric Walker are very accomplished developers, with 20 titles and 14 shipped games between them, these are not your squeaky-voiced 15 year old recording themselves getting lost through the interface and narrating as they go. The tutorials also teach basic project management, workflow, and development practices.
After all that introduction, they throw you into the pool feet-first and get you into making games. The next lesson, Game Development, Project 1 is a point-n-click-n-kill game.
Game Development, Project 2 is a space shooter asteroid clone.
Following this is a lesson in Unity3D Tool Development, in which you learn to create various game utilities, such as timers, score-keeping mechanisms, sprites, and more.
In the next segment Making Your First Real 2D Game, the Walker brothers guide you step-by-step through the process of creating a 2D Mario clone.
And finally, to put all of those above-learned skills to use, is the ultimate challenge, a 3D Mario Clone.
They also have some other Unity3D tutorials around Exporting/Importing (workflow) and publishing your final product online.
These are all setup as an educational course, with lab materials, and a certification you can earn by submitting your finished games for viewing by the public.
And as a bonus, there are a slew of other tutorials on creating basic design, concept art, speed painting, character, weapon, vehicle creation, 3dsmax tips, and a whole lot more! If you want to learn about the basics of creating art for games, this is a great place to start.
Great stuff, really love their learn-by-doing approach, which is how we learn best.