Blender is the best free software video editor across GNU/Linux, Windows and Mac. I've used it to edit a feature length movie. It's not perfect at all, but doesn't crash and doesn't crap out when you give it a slightly unusual formatted file.
I third this. It's one of the best tools out there for video, and it's hidden in what most people refer to as a 3D content creation suite. I've used it professionally to good result.
I edited lots of screencasts in Blender. Can confirm it's more than suitable and above basic. There is a complete series on Youtube on how to use Blender for video editing.
Looking at the documentation, I was under the impression that all it could do was basic cutting and simple things like cropping. Can it do simple effects, like video overlays?
Yea, there are lots of effects and tools hidden in there! I've been able to implement every effect I've ever needed without much effort. I actually have been using blender since I was a kid so I know my way around better than most. I'll edit this comment later with some quick tips or examples.
Sorry for the shortness of this, but I know everybody strapped for time and might find this handy.
Things Blender capable of for video:
* Advanced graphical node based compositing
* "Effects Strips": Essentially generates a strip in the sequence editor that you can layer above the target media strip. Like using a Photoshop layer for one specific effect.
* Decent audio mixing capabilities
* Fantastic motion tracking (advantage of being built into your creation suite)
Pro Tip: Make sure your output frame rate is the same as the videos you are going to import. Otherwise the audio gets out of sync.
Blender is an amazing piece of software, although I've only used it for the 3D modeling and animation features. The flexibility of the UI is something I wish more software would adopt.
