The free plan is limited to 60 objects, no revision history, no Visio import/export, and can only publish as HTML, PDF, PNG, JPEG. Check out our review of Lucidchart for a more in-depth look at what it can do. It's web-based, so you can access it from anywhere, and packed full of features that make diagramming easy. LucidChart - A very solid alternative to Visio in a lot of ways.It has an automatic layout feature that can instantly rearrange a diagram to be clutter-free and more readable, which is fantastic for big and complex flowcharts. yEd Graph Editor - Very similar to Dia, except much more powerful and proportionally harder to use.
Keep in mind that these are NOT open source unless specifically noted in the description. Dia and Draw may be the best available right now, but a quick web search will turn up plenty of competitors that are just as good in many ways.