ParticleIllusion!

With Adobe After Effects software, you can create compelling motion graphics and blockbuster visual effects with flexible tools that help save you time and deliver unparalleled creative power. It's used in the post-production process of filmmaking and television production and its main uses are the origination of 2D and 2.5D animation, visual effects compositing and finishing (image adjustment, color correction etc.). After Effects can also be used as a basic non-linear editor and a media transcoder. »

HitFilm merges FXHome VisionLab Studio , FXHome Effectslab and FXHome CompositeLab into one software.

Blackmagic Fusion (formerly known as Fusion and eyeon Fusion) is an image compositing software program created by eyeon Software Inc, now developed by Blackmagic Design. It is typically used to create visual effects and digital compositing for movies, TV-series and commercials. It employs a node-based interface in which complex processes are built up by connecting a flowchart or schematic of many nodes, each of which represents a simpler process, such as a blur or color correction. This type of compositing interface allows great flexibility, including the ability to modify the parameters of an earlier image processing step "in context" (while viewing the final composite). Upon its acquisition by Blackmagic Design, Fusion was released in two versions: the freeware Fusion, and the commercially sold Fusion Studio. »

Liconcomp allows live content compositing to display screens for digital signage, scoreboards, LED installations, ....

ButtleOFX is a simple, user-friendly and open source compositing software. It is based on TuttleOFX,  an open source, modular and sustainable image processing architecture.

Export the particle effects as static animations onto sprite sheets, animation strips or image sequences in PNG format, or if you develop for the iPhone or iPad, you can export using the PVRTC format (Mac only). If you program games using the powerful Blitzmax programming language, you can also use the effects directly using the TimelineFX Module.

Motion is a compositing application used to create and edit motion graphics, titling for video and film production, and 2D and 3D compositing for visual effects.

Autodesk® Smoke® software is a leader in editorial finishing for high-quality commercial and broadcast projects. Smoke offers an end-to-end finishing toolset that combines intuitive timeline navigation with advanced 3D finishing tools. Native support for industry-standard media formats and GPU-accelerated interactivity when compositing means you can finish projects faster and deliver your best work even against tight deadlines.

With veejay, you can play the video like you would play a piano

Synapse is a free node based compositor for Linux and Windows.