Several low-cost, or no-cost video editing applications are available to enable you to perform some basic editing of your smartphone videos.
iPhone users can get CuteCUT is available on iTunes as a free download or for $4.00 you get the version without their logo appearing over your video.
Video Edit, also for iPhones costs $2.99. With it you can assemble your clips and trim them, but it lacks effects and transitions.
Have an Android phone? Then try the free Magisto Magical Video Editor. It includes special effects and even music. This app requires you to sign up for an account before you can save your movies.