I've done a bunch of little mini-tutorials on Mac Break. If you are new to Motion 3, they provide quick overviews of some key features.

Click the photo to go to the tutorial.
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3D Groups

Time Remapping

3D Paint

Tracking

Templates

Custom Icons

Mixing 2D & 3D

3D Space

Audio Behavior

Motion 3 Video Tutorials from Apple
Motion 3 Video Tutorials on MacBreak
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"Making Your Design Move with Motion"

A short video showing how to import and animated layers Photoshop files.
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NAB 2007 Launch
FreshDV.com has a video of Apple's demo for Motion 3 that was shown during the launch at NAB in April 2007. The video quality isn't terrific, but it's bearable. And the demo really gives a good indication of how Motion's 3D environment works.
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Feature Overview Videos

On Apple's site, there are 8 short videos that give an overview of some of the key features in Motion 3, including 3D space, retiming behaviors, audio behaviors, tracking and match moving, text behaviors, paint and templates.
Motion 3 Video Tutorials from dvcreators.net
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Josh Mellicker at DV Creators provides a tutorial on Motion 3's new motion tracking feature.
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Another cool little web video tutorial on one of Motion 3's new features. Very nice overview of the different light options and how they work.
Motion 3 Video Tutorials from motionsmarts.com
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Other Motion Tutorials
Motion 3 Tutorials from me
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Image Masks and Gradients

Why your Motion text looks bad in FCP

The reflection effect

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Creating reflections with image masks

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Creating titles

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Trimming behaviors

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Importing Photoshop and Illustrator files

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Creating billowing fabric
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Image Masks and Light Wrap
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Motion, Final Cut Pro, and anamorphic footage
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Importing Motion projects into After Effects

Using tracking to create a write-on effect

More on tracking

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Creating billowing fabric

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Image Masks and Light Wrap

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Motion, Final Cut Pro, and anamorphic footage

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Importing Motion projects into After Effects

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Using the ImageFlow Fx plugin

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Motion's filters

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Using Motion templates in FCP (M3 only)

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Using Paint (M3 only)

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Converting behaviors to keyframes

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Growing vines

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Wormhole

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3D Shatter (M3)

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TV Look

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3D & the F key

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Retime Particles (M3)

City Timelapse

Title Project

Write On Effect (M3)

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Animating
Photos

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The Replicator

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Create a Picture Wall

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3D Layers

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3D Camera