These video apps are popular with mobile journalists and smartphone filmmakers. These are the ones I recommend in my workshops and online courses that teach smartphone filmmaking.

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Filmic Pro (Android and iOS)
The best app to have.
Hyperlapse from Instagram (iOS)
Cinema FV-5 (Android)
Filmic is better but this is cheaper.
Filmic Pro app can also control hardware like the DJI Osmo Mobile gimbal to provide stable, smooth 4K video capture. An iPhone 6S+ Røde VideoMicro plus SC4 adapter shown. (plus a cold shoe mount)
LumaFusion (iOS)
Professional multitrack video editor. (See photo below)
Power Director (Android)
Professional multitrack video editor.
Gravie Text on Video (iOS)
Handy for adding watermarks and text over videos.
iMovie (iOS)
Reliable, but does not support 25p.
Quik (Android and iOS)
Social video editor. Quirky, but fun.
Vlogit (iOS and Android)
Splice Video Editor (iOS)
Great for editing rushes .
VideoShop (Android, Windows and iOS)
Very basic, but free.
Kinemaster (iOS and Android)
Non-standard UIX, watermark version is free, monthly subscription.
VideoPad (iOS and Android)
Free 2-track video editor with voice over and 25p support. Slow, awkward UIX. Ads.
The non-standardization of Android devices requires each user to make their own trial runs with apps that will work on their unique mix of device, chipset and OS.
Android student users report that full video production is more capable with the late-model flagship models that have the advanced chipsets.
Smartphone Filmmaking: LEVEL ONE – Film & Edit Mobile Video
(The $10 coupon offer – expires soon!)