it is mandatory to hold a valid ticket in local lines Rex,R, OR S-Bahn ?

Rail passes don't generally cover local buses and metro services. Many S-Bahn services are included.

I bought a rail pass back in the 90s, but these days I only buy point-to-point tickets.

Besides the great info here on Rick's website, seat61 has a good details on the Eurail Global pass as well: http://www.seat61.com/Railpass-and-Eurail-pass-guide.htm#Understanding-the-Eurail-pass-range

In Germany, for sure, and I think also in Austria, the S-Bahn is technically a regional train, so a railpass should be valid. There used to be one S-Bahn line in Berlin that didn't accept rail passes, but I'm not sure that is true anymore. I do know that rail passes are not accepted on the trains of the Bayerische Oberlandbahn.

Hi,

You saw the sign in Austria "Nur mit gütigem Fahrschein." or "Mit gütigem Fahrausweis." The Pass doesn't cover these U-Bahn routes. For the regional trains RB and RE the Pass is valid.

For the S-Bahn in Germany the Pass is valid, don't know about the S-Bahn in Vienna. My hotel gives me a "combo ticket" covering all transit with the city limits in Vienna, no need to worry about the proper ticket, etc.

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

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).

Bravo! A very good point on using the rail Pass after arriving in Berlin, esp early morning, then using it to ride all over the city. That never occurred to me in maximizing its use.

using the rail Pass after arriving in Berlin

Yes, if arriving by rail and already using the rail pass that day, but if not already using the pass that day, it is probably less expensive to buy a local (VBB) transit pass than to use a day of your railpass.

A rail pass will cover travel in cities on the S-Bahn, which is run by German Rail, but not on other means of transport, like U-Bahn, trams, and buses, which are run by the local transit authority.

True - if your pass is for X number of days and not a consecutive one then it it is a waste of a day to use just for S Bahn.

A valid rail pass is your valid ticket (e.g., using one of your counted travel days). Eurail passes cover all regional trains operated by the national railways and also many that are technically private/regional railways. Also covers the S-Bahns in German cities (with limits in Berlin) and in Innsbruck and Vienna and private WestBahn trains in Austria.

See the coverage map that comes with your pass as well as

https://ricksteves.raileurope.com/rail-tickets-passes/eurail-global-pass-free-day/index.html and

http://www.eurailgroup.org/German%20Private%20Railway%20companies%20overview.pdf - not easy to read but it should convince you that you have lots of coverage.

I think I have seen that sign for the S-Bahn between Innsbruck and Wörgl. There is no conductor from whom to purchase a ticket on the S-Bahn (only an occasional fare police). You have to buy you ticket from the automat on the station platform before boarding.