I always rely on Highcharts, probably the biggest library presented here.
Fit all the case (except map maybe) and flexible enough to let you change everything if you or your designer want something very specific !
Fit all the case (except map maybe) and flexible enough to let you change everything if you or your designer want something very specific !
Highcharts was the first library I found where, even when I assumed what I wanted to do would be impossible, it could do anything I threw at it. The number of settings and formatting options is incredible. Such a fantastic library.
(By the way, for maps, there's Highmaps. It's an additional license fee but it integrates nicely and provides a bunch of cool choropleth map features, etc).
It's extremely customisable and has tons of readymade fiddles[2] and business dashboards[3] for inspiration(ready copy). I recently used full code of one of their dashboards for my project. I've never failed to convert my designer's or PM's concept into exact same working code with FusionCharts. Highly recommended.
[1] http://www.fusioncharts.com/
The only downside I dislike about flot is that it depends on JQuery. As I otherwise don't rely on JQuery at all, it means another ~80kb of additional JS code. Beside that, flot seem to be a very good free alternative.