Eurail Global Pass - Is it valid for travel within city local transport?

Eurail Pass Explained

In general the Eurail pass is valid on train lines only. Metropolitan public transport is usually not included in such rail-passes. The Man in Seat 61 says:

Railpasses cover all the trains run by the main national train operator in each country covered by the pass, including local trains, suburban trains, regional trains, inter-city trains & international trains. [...]

Railpasses don't cover city metro/underground/subway trains, trams or buses as these are usually run by urban transport authorities, not by the national rail operator.

Having said this, note that Eurail has a page listing benefits per country. From there you can gather all the information required for your trip. All in all, it's up to you to figure out if this is a viable option, depending on your itinerary and budget.

Benefits in Germany

To give you a few examples, the benefits for Germany include travelling on S-Bahn trains:

Hop on the S-Bahn and discover major German cities

A Eurail pass is also valid on the S-Bahn (suburban metro railways) networks that DB operates in major German cities. The S-Bahn can be recognized by its logo (a white S on a green background)

S-Bahn Validity in Berlin

Others have mentioned that the pass isn't valid on Berlin's S-Bahn. I coulndn't find any mention of this, but I welcome edits. The Eurail webpage for Germany however says that the pass is indeed valid on the S-Bahn, and it mentions a station in Berlin:

Your Eurail pass is also valid on the S-bahn rapid transit system. Take the S-Bahn to Bahnhof Potsdamer Platz for the panoramic observation deck.

Moreover, this post on a related thread from Rick Steves' dating December 2014 says that the Eurail pass should be valid for the Berlin S-Bahn routes:

The Eurail pass includes all S-Bahn that are run by German Rail. That might now include all; at one time there was a line in Berlin that was not included.

Benefits in Austria

The same benefit seems to apply to Austria. Indeed the Eurail pass allows to travel for free on the S-Bahn in Vienna and Innsbruck:

Get free transportation on the S-Bahn

Eurail pass holder can travel for free on the S-Bahn in Vienna and Innsbruck.

Benefits in France and Italy

The benefit pages for France and Italy however mention nothing of the like.

It is hard to advise for or against Railpasses, such as Eurail or Interrail. The Man in Seat 61 lists some arguments.

Without knowing where you want to go, how flexible you want to be and how old you are, it is difficult to advise for or against.

There is also a thread on this site: What is preferable, Eurail Pass or Buying Pass on the spot?

In principle, the Eurail pass is not valid on local transport networks. There are however exceptions. For example, in Germany, the pass is valid on the so-called S-Bahn. These are networks of suburban trains that you can find in any major city.