I worked in the automotive wiperlab at ITT Automotive for while as a wiperlab technician.  We developed windshield wipers for all the top brands, mercedes, ford, chevy, toyota, etc.

After our road grime tests, and after hundreds of thousands of wipes across a windshield, your windshield develops a residue that is sticky and prevents your wipers from working correctly.

The product we always used to clean Windshields was Bon Ami cleanser.  It doesn't scratch, and is excellent at removing greasy grime and rubber from a windshield.  I've used it ever since on my own automobiles, especially at wiper change intervals.

To do this, first remove the major dirt particles by hosing off your windshield and cleaning like you normally would.  Then you cover your windshield with Bon Ami cleanser (has a little duck on the front) and use a non-scratching sponge, or cloth, and water to clean the windshield with the Bon Ami.

*Note, the inside of most automotive windshields is layered with a film that my scratch if used on the inside of the window, so this is only for the OUTSIDE of the automotive window.