The best way to get started if you know nothing about Unity is to go through the 3D Platform Tutorial. With this in-depth tutorial you can learn how to make a 3rd person platform game in Unity, but at the same time you will learn all the basics of Unity that will give you a head start when creating your own game.
Unity Locomotion system
If you are doing a lot of character animation in your game, you must check this out. Rune's Locomotion system was presented at GDC 2009 in a fully packed session. The great thing about it is that it does stylized IK, meaning that it uses the existing animations to do good looking motions and only minimally adjusts them to place feet on the ground etc. It also scales really well, you can start out with a simple walk cycle and it will automatically synthesize sidestep / run / backwards animations for you. If you provide more animations the animations will simply look better.
Get the project folder here
Watch the Unite 2008 talk here.
Visual Studio Integration
In our roadmap we announced Visual Studio integration for Unity 2.6. However you can already use Unity with Visual Studio very well. Lucas Meijer has a blog post on how to create Visual Studio projects from a Unity Project folder automatically here.
Amir's Unite 2008 Shader talk is the defacto best tutorial on building shaders. He reshot the session into a 2 hour talk so he could go through all the details.
Customizing the asset pipeline
Lucas is really into tightly controlling the asset pipeline and automating every single bit. Fortunately Unity is very extendable, so he has a lot of places where he can plug in. Watch the talk here.
Matthew's Physics Talk at Unite 2008
I generally love hearing Matthew's talks. Got to love the pictures. This year on car physics was very useful.
Nich's Unite 2007 talk on how to create your own GUI controls is still very relevant.
The wizkid Forest talks about particles
Forest Johnson, a (then) 15 year old kid single handedly programmed the Avert Fate demo, he did some awesome particle effects too and then gave a kickass impromptu particle talk at Unite 2007.
Blogs about Unity:
The Flashbang guys have an awesome blog about Unity, that contains deep technical information that sometimes even I didn't know about.
Lucas has a great blog about Unity with a lot of very useful information.
Somebody made a site collecting video tutorials about Unity.