Chromic is a free iPhone app -- with the seemingly inevitable in-app purchases -- that provides some very high quality filters for the videos you've already created, and it will also provides the opportunity to shoot live and render effects later.
The app includes 8 built-in filters, and filters can be purchased in sets for US$0.99 or $5.00 for all 54 of them. The video player runs full screen in landscape mode on the iPhone, and scrubbing is done by swiping your finger back and forth on the video. When you are done, you can export the rendered movie to your camera roll.
The quality of the filters is very high, as the software imports your movie as a "digital negative" and then adds the filter from there. Effects are nondestructive, and before you render them you can try several options.
The free version of Chromic will work well for most people, but some may want more capability. The add-ons are reasonably priced and grouped by type of effect, so you won't waste any money on effects you will never use.
Chromic Video Filters
Of course other apps like Instagram provide some video filters for free, but I like the look of these filters and think it's worth having the app as an option.
Chromic requires iOS 6 or greater and is optimized for the iPhone 5 series of phones.