Making map where overlapping symbols increase Opacity?

You can do it in QGIS using symbol transparency, feature blending mode and symbol color.

Notice the difference between Layer Transparency and blending mode(that will be applied to all features) and the symbol transparency and feature blending mode that will stack with other features in the same layer.

All seetings are available in Layers Properties > Style.

With the value of 95% of symbol transparency, the chosen color for the line will be totally opaque only when at least 20 features overlay each other. This number is limited to a 100 features overlay (tranparency 99%).

UPDATE: Following Nathan advice, using different blending modes (like multiply and addition) other effects can be achieved.

Duplicating the layer, with different line colors and using modes like dodge in the layer blending, can give some nice effects.

I'm not sure for the first example, but the second one is an image of the line density (a raster data created based on a kernel that produces an weighted sum of the lines in a neighborhood).

in practice, you can do it with arcgis line density (spatial analyst) and you will find open source hints here

EDIT: the first example was thus well lines with a feature transparency. This is not feasible in ArcGIS (you can set feature transparency for polygons, but it does not add to each other for overlapping polygons of the same layer. In theory, of course, you could make one layer per line...). So +1 for QGIS...

You can also do this in Tilemill using the following:

line-comp-op: plus;