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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Feature Overview Videos

On Apple's site, there is a great overview and several short videos that give an overview of some of the key features in Motion 3, including a QuickTour, Behaviors, Keyframes, 3D, Text, and Particles.
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

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3D Cameras and Photoshop Layers