I want something like Axiis, but without using Flex or other Adobe products.
The closest I can think off the top off my head is Google Visualization API
Of course, AFAIK, this will only work for on-line applications. And is Google any less evil than Adobe is a question for you to decide :)
Have a look at the JavaScript InfoVis Toolkit. Also, maybe the gRaphaël charting library (built on top of Raphaël) can suit your needs.
Others:
- Ajax.org
 - Google Chart API
 - flot
 - Style Chart
 - Bluff
 - JS Charts
 - jqPlot
 - pChart
 - ExtJS
 - Vizualize
 - TufteGraph
 - milkchart
 - DojoX Data Chart
 - jQChart
 - PlotKit
 
See whether one of these suits your needs best.
Hey oo...
This is a pretty open question, as you havent specified any preference for any particular technology or language.
I do a lot of WPF/C# stuff so I immediately start looking on that stack. Assuming that this would be a suitable platform, then Visifire might be worth looking at... I originally found them here on codeplex.
There seem to be a ton of third party paid for components that can do similar things. Telerik has some visualization tools that may also be worth having a look at.
Is thre any specific scenario that you are looking at, or any specific language? I think we may be able to suggest better alternatives if that was provided.