I would like to make the value of a node, say a blur node, influenced by the distance between two objects (say a camera and a cube) with blender render engine. How would you achieve that?
Yes, with Drivers
You can animate a property with a combination of values of other chosen properties.
To set up a Driver, just right click in the parameter field and choose "Add Driver"->"Manually create later" from the pop up menù. In the following example I added a "value" node and linked and added a driver to control it's value (the purple one), but I might have directly controlled the Size parameter of the Blur node itself:
In the Graph editor, under the Driver editor type, you can easily set up a Distance Driver Type and pick the two objects (camera and cube in the following example):
Here's the result: