It looks like you want to have general-purpose graphics, not specifically the kind of charts visualizing mathematical functions, which is one of the most common understanding of the term "chart". In fact, this term is much wider that that, so you should have explained what exactly you need, or just mention more general term "graphics", "vector graphics" or the like.
First of all, I would recommend to use HTML5 Canvas feature:
http://en.wikipedia.org/wiki/Canvas_element[
^].
These days, I think, this is a base approach for the cases when you use just the server and the browser, without Java or Flash technologies, which are the separate topics.
Please see what one can do, this is pretty impressive:
http://net.tutsplus.com/articles/web-roundups/21-ridiculously-impressive-html5-canvas-experiments/[
^].
But you can find something more specific to diagramming:
http://bit.ly/18sK2WR[
^].
—SA