[edit] Some commentary:
I've used Fusion Charts in the past (on tweetstats.com) and it provides some good looking and easy to implement charts. That said, it's Flash but it was the best looking option around when I implemented it back in late '07. Since then, there's been a nice rise in JS charts. gRaphael is amazing, but somewhat buggy and lacking documentation. Highcharts seems very complete and well-documented. I only came across Protovis recently, but it seems pretty darn awesome.
we use protovis for our graphs and it is pretty damn awesome. The cross-browser support (no IE) is an issue until IE 9, but it's pretty incredible stuff. I'm no designer but they make it easy to make pretty complex charts.
The lack of IE support is what kills it for us. We need to do some charting stuff, and we'll probably end up extending gRaphael or Grafico or something and copying several of the Protovis charts.
performance hasn't been an issue. The demos are some pretty intricate stuff and for the most part not made for performance. Even most of those have been speedy.
I made Grafico: http://grafico.kilianvalkhof.com it's an opinionated SVG charting library with excellent documentation and lots of customizable options.
I'm on the ZingChart team - we render charts in both HTML5 and Flash. So far we've gotten great feedback. Our charts are JSON driven and can plot huge data quickly [demo] http://www.zingchart.com/labs/blog_charts/10k_points.html.
Plug: Give my startup Pretty Graph a try (http://prettygraph.com). We are trying to build the best web-based graphing tool. Still in very early stages, and looking for early users. I was going to make a review post here soon, but since you asked now I thought I should mention it anyway.
Ha! I'm aware of that. However, I think the format of the graph output is not the most important/unsolved/annoying problem in making graphs from my users' perspective. The key difference here between our product and the other libraries and apps mentioned in this thread is that we are primarily building an end-user application, not just a library for developers to use (although our API will also allow that).
I may be proven wrong and have to move to SVG/VML, but only time will tell. For now our focus is to build the best tool to put any kind of data in and get pretty graphs out.
if you're on a .Net platform, you may want to take a look at Dundas Data Visualization http://www.dundas.com. Just try to avoid the defaults :) We use these for data vis at http://allegiance.com.
[edit] Some commentary: I've used Fusion Charts in the past (on tweetstats.com) and it provides some good looking and easy to implement charts. That said, it's Flash but it was the best looking option around when I implemented it back in late '07. Since then, there's been a nice rise in JS charts. gRaphael is amazing, but somewhat buggy and lacking documentation. Highcharts seems very complete and well-documented. I only came across Protovis recently, but it seems pretty darn awesome.