Keywords: flash, swf, charts, financial charts, PHP, server/client, statistics, dcflash, actionscript, xml sockets, marketing, data visualization
I have an actionscript charting library (called "dcflash"). You can see some demos of it. (I have some more sophisticated demos not released publicly. If you would like to see them please contact me directly.) This library has generated a lot of interest and parts are gradually being released as open source: late 2006 saw a first release on sourceforge: http://dcflash.sf.net/.
Most applications so far have been in financial charting (described in its own section). The charts have also been used in marketing applications (see the pie chart demo) and in data visualization (try the "graph" links in the MLSN results page).
Not charts exactly, but I have also generated exhibition maps (over 500 maps: one for each exhibitor, hilighting their booth), using data from an SQL database. For each exhibitor both an interactive flash version and a static gif version. The maps were re-generated automatically each time the database was updated.
For connections to the back-end live data source I have typically used XML sockets. I have found these efficient and flexible, and therefore most useful. Incidentally my fclib library contains a free PHP xml socket library that works on all of linux, windows and mac, and has been useful for a number of quite diverse projects.
HTML5 looks quite promising to be used instead of Flash for this kind of charting. However it is less efficient (more CPU cycles, more memory), so when the amount of data goes up the charts can end up more sluggish than the same chart written in Flash.