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):
Numerous fixes as usual.
Changed shortcut for Add Video Track to Ctrl+I.
Changed shortcut for Redo to Ctrl+Y on Windows.
Added 10% to the player zoom menu.
Hide the VUI (video user interface) when the play head is not over the clip with the current filter.
Renamed the Rotate filter to Rotate and Scale.
Keyframes are now saved in the project file using time clock values instead of frame numbers to make them adaptive to frame rate.
Reverted memory manager change from v18.05 pending further testing to improve stability.
Added advanced keyframes to the Size and Position filter.
Added simple and advanced keyframes to the following video filters:
Rotate and Scale
* = including the (still experimental) GPU filter
Added Copy Timeline to Source to Timeline menu.
Changed the audio codec to AC-3 for the edit-friendly and reverse MP4 file format.
Changed J and K key behavior to change speed up or down before changing direction.
Added categories to the Export presets (custom presets can start their name with “category)” to use a category).
Added View > Layout menu for custom and stock layouts:
Changed the default, first-time user UI layout to Timeline Project.
Changed Properties > menu > Reverse… to work on a trimmed clip from either Source or Timeline.
Added Properties menu items to the context menus for Timeline and timeline clips.
Added logic to sort GoPro files when multiple files are opened or dropped.
Added support for setting project file name (using File > Save) for empty project.
Added search field to the filter chooser in Filters.
Upgraded MLT to v6.10.0
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.