You asked, and herewith my opinion:

No, they aren't worth it, or rarely are. Buy point-to-point. Since you rarely can buy cross-border tickets from any individual country's rail network website, and since raileurope is nearly always ridiculously overpriced, wait until you get overseas. The last time I needed a cross-border ticket (Verona - Innsbruck) was last April; I couldn't buy it off trenitalia.com, so I bought it in Venice. I bought it 6 days in advance, but there were plenty of empty seats (travelling on a Wednesday morning). Rail agent sold us a special for two people travelling together - in short, there are deals available that save you money outside of any theoretical rail pass savings. ( I say theoretical, because my idea of a trip is not spending all of it on a train, which is about what you have to do to get a railpass to break even.)

For many trains, you end up having to pay supplements and/or get reservations in additional to the pass anyway, so there goes the so-called 'convenience.'

The costs for doing this in some countries, notably anywhere in northern Europe or Switzerland, will rack up very quickly.
Supplements can be paid on board. Trains that absolutely, positively require reservations are few and far between, and unless you're in peak season on a peak route there's little reason to get them if they're optional.

And for me, the greatest attraction of a rail pass is the flexibility, especially when exploring a new region. Want to stay a little longer? No problem! Don't like the look of a town? Hop on the next train out! Sunny day? Take a train to the beach or the mountains. Rainy today? Head back to the city.

I would ignore this kind of advice.

Instead, it's best to determine for oneself, based on one's own plans, whether a pass makes sense. (And I actually HAVE purchased, and made good use of, a Eurailpass, several years back. On other trips to Europe, though, I DIDN'T purchase one. The decision was based on comparing the cost of point-to-point tickets with the cost of the pass. And I did NOT spend "all" of my trip on a train to make the pass pay when I did buy one!)

Once again, read my reference in post 11. Rick Steves and staff have compiled a truly helpful resource on European railpasses.

Dordal , would you be so kind as to tell us how much you are going to pay for your Eurailpass? and also your age? I'll try to find out how much you would have to pay for tickets as posted in the opening post.
This thread could go on for ages with each time one poster being against and one for it... As I am in Europe, I can make a few phone calls to find out what will be most adantageous to you.

Good idea!

One reason I posted the link in post 11 (Rick Steves Guide to European Railpasses) is that it assists you in estimating the cost of point-to-point tickets for your expected itinerary.

However, one of the magical things about railpasses, at least if you get the unlimited, consecutive-day kind, is that you are then free to take little extra side trips and day trips without worrying about the rail cost. Also, I was inspired to travel farther afield than originally planned (to Copenhagen for a couple of days and then up to Stockholm for a few, even though my original trip plan was no further north than northern Germany). The cost of an overnight couchette at the time was less than $20 supplemental, far cheaper than the hotels I normally stayed at, so this was a "bonus" as well. I had about four or five overnight train trips in all on this particular trip; some were in the cheapest couchettes, and others were in more comfortable though somewhat more costly digs.

I realize that the OP may not be planning to purchase this type of pass (vs. the more limited "X days in a given time frame" pass), but the above is something to think about for anyone who is considering the more classic type of pass. Some of the spontaneous "day trips" I went on were quite lengthy (Munich to Bamberg and back in one day), since I had the prepaid fare in my pocket. @:-)

To my way of thinking, the real value of an overnight train trip in a couchette (or even a sleeper car) is not just the fact that you don't have to pay for a hotel room, but that you can get from one place to another while you'd otherwise be sleeping. Spending good "being-there" time in transit is more expensive than money.

Do your homework on the Internet before you decide. A Eurail pass is a good idea if you will use it enough, but you can save a lot if your travel schedule isn't too heavy. Every country has a web site for its train system. In Italy, for example, it is trenitalia.com. You can look up train schedules and fares easily.

In my opinion, EURRAIL passes, which at one time were a bargain (20 or 30 years ago ), have gotten to be too expensive. [You are paying for countries you may never visit.]
EUROPASSES, which give you a limited number of days in long period, can prove to be very cost effective. In many cases with proper planning the 3, 4 or 5 country versions can be the cheapest. Sometimes dedicated country passes could be real prize winners.
Overnight trips in coach used to be the biggest bargains, you get from point A to point B, arriving early in the morning, having saved a night in hotel costs (sometimes feeling like a pretzel, if you share a compartment with 5 other people...). The European rail network have added so many high speed lines that finding overnight trips (in coach only) is becoming very difficult; it is now also very hard to find first class coaches on overnight trains.
Even with some of the negatives I have noted above, the balance tips in the favor of a railpass over individual tickets if for no other reason than the fact that you can go to interesting places at the spur of the moment--and this is what makes travel exciting.