I don't know about the others here, but I've tended to use a pipeline consisting of:
1. Render to individual pngs from Mandelbulber, UF, custom code, etc., often at high resolutions (e.g. 8400x4725) for high quality AA.
2. Use a bunch of my own developed software to combine slides/clips generated in 1 to a single huge image stream -- say, 15000 numbered pngs at 1280x720 (720p high definition).
3. Use Audacity, own recorded sound effects, and possibly some public-domain music (e.g. pre-20th-century classical performed and recorded by a US military marching band), to construct soundtrack.
4. Use Virtualdub and the x264 codec to convert the outputs of steps 2 and 3 into an .avi or suchlike.
Virtualdub provides only a few no-frills editing capabilities, so my step 2 is where much of the "interesting" video editing stuff gets done (title cards, still images->slideshow, transition effects, keyframes->zoom movie, etc.) after the fractals themselves are produced in step 1.
https://www.youtube.com/v/XgvaWmDDct4&rel=1&fs=1&hd=1 was generated in this manner:
1. A relatively small number of still images and zoom keyframes, plus one clip of a Julia set morph. The mini-map and dot in the Julia morph was done within the fractal software's layer/animation capabilities.
2. Everything else in the video was done using about 1000 lines of Lisp code to implement a DSL for processing streams of images in various ways, and then using a short program in that DSL to transform the output of step 1 into all of the video's frames.
3. A few sounds recorded around the house, plus Audacity to synthesize some more sounds and glue everything together, produced the soundtrack -- no third-party content was used there at all for that one.
4. Virtualdub + x264 + mp3 from step 3 + directory of fifty gigs of pngs from step 2 = video file ready for upload to YouTube.
These days, there are increasingly capable movie editors for PCs and Macs that could be used for step 2; however, they're not 100% substitutable with what I've done, as what I've done is more like the LaTeX to their word processors.

HTH.