Are Eurail passes valid on any trains?

A Rail pass is generally not good value in Italy, as tickets are relatively inexpensive there.

To answer your question, Rail passes are valid on Intercity trains, however these do not include the compulsory seat reservations. You'll have to buy those separately. That also applies on the Freccia high speed trains. If you're caught without a valid reservation for the train you're riding on, you'll face hefty fines which will be collected on the spot.

The Regionale trains (such as the Cinque Terre Express) do not require reservations. However you'll probably find that the daily cost of the Railpass is higher than the cost of locally purchased tickets.

If you decide to buy tickets from a Kiosk, you'll need to know the correct spelling of the destination towns (ie: Vernazza).

There are a few private rail operators in Italy that don't accept Eurail passes. They're listed mid-page and on the side bar at https://www.ricksteves.com/travel-tips/transportation/trains/italy-rail-passes. Faster trains stop at Monterosso or perhaps other Cinque Terre towns, but other connecting trains within the Cinque Terre are regular Regional trains run by the national railway. They're covered by passes if you're using one of your counted rail pass travel days.

The term "Cinque Terre Express" may be used by Cinque Terre marketers but is not particularly important or seen on schedules at Trenitalia.com nor the all-Europe timetables provided by DeutscheBahn.

Thank you for the information on reservations and intercity trains. We are also going from Venice to Salzburg and the cost of that ticket alone will make it worth buying the pass the 4-day pass.

We are also going from Venice to Salzburg and the cost of that ticket alone will make it worth buying the pass the 4-day pass.

The eurail site shows the 4-day pass for Italy and Austria as $340 at https://www.eurail.com/en/eurail-passes/select-pass/two-country/austria-italy

RailEurope, which usually doesn't even show the cheapest fare, shows Venice to Salzburg for $58
http://www.raileurope.com/train-tickets/journeys/article/venice-salzburg

not sure where you got the info that the pass is cheaper...

to echo the Venice to Salzburg is only 49 euros; you may not need the well marketed it seems overrated Eurail pass

Venice to Salzburg is only 49 euros
That's true, but only if you buy them in advance at the websites of the Italian or Austrian railways. There are two routes from Venice to Salzburg: one via Villach and the other via Verona and the Brenner pass. Both routes are very scenic.
And don't make the common mistake you need 1st Class to enjoy these train rides. Second class is just as comfortable.

John's research doesn't consider the discount for two traveling together. That rate is $281 per person for 4 days in 2nd class.

As always, railway knowledge is summed up by www.seat61.com
Discussions of passes often note that main-line trains may require reservations and those must be purchased separately. I'm with the side of the argument saying that rail passes are often not good value. Only you can solve that debate for yourself by checking, individually, the point-to-point costs (which will include reservations in the purchase price.) Best info comes from the rail companies themselves rather than RailEurope, a secondary vendor. Seat 61 says so too, even though his site sells RailEurope (like Steves).

Eurail passes are RARELY make sense.

Different strokes for different folks!

If two people are traveling together, and want to travel in First Class, a Eurail Pass can save you some money - especially when you plan on taking some really long train rides.

I suggest making any required reservations at the same time you buy the pass.

I use a rail pass but would not for Italy. If you are doing a long ride on the TGV in France, better to waste the extra Euro on a 1st class reservation. I would.

So I re-checked the rail pass prices - when I requested a price for 1 adult and two children it gave me the price for just 1 adult (I thought the price they gave me was for the three of us). If I were to buy an adult pass and a youth pass (plus one free child), the price is more expensive than buying point-point. Glad I checked more carefully.
Thanks for all your responses!