Shotcut is a free, open-source and cross-platform video editor.
The program uses the popular FFmpeg to import source files, which means there's no need to worry about format support: it'll open just about every video variant that's ever existed.
There's also support for capturing resolutions up to 4k from SDI, HDMI, webcam, JACK & Pulse audio, IP stream, X11 screen and Windows DirectShow devices.
A straightforward interface ensures you'll be up-to-speed immediately, and offers plenty of ways to customise your working environment.
There are lots of video filters, from simple colour/ brightness/ contrast tweaks, fade ins and outs, transitions and so on, to special effects, video compositing and blending modes, chroma key, HTML overlay and more.
Shotcut offers almost as many audio effects and filters, with fades, balance, bass and treble, band pass, delay, downmix, normalize, pan, reverb and more.
All this is editable on a highly configurable multitrack timeline, then exported in whatever video format you need.
18.07.02 adds (see changelog for more):
Shotcut isn't for the complete video editing novice, but it's not difficult to use, and if you're willing to spend time learning the basics then there's a lot of power just waiting to be unleashed.