Eurail pass or train tickets

There's no easy answer to this, because it depends on what journeys you want to do (how many, how far, over how many weeks and which part of Europe). A rail pass price is fixed whatever journeys you make with it, but point-to-point prices vary enormously in price, some are cheap, others expensive, depending on the distance, the country, when you buy them, and whether you book a cheap ticket in advance or a more expensive ticket on the day. But here are the "rules of thumb":

1. If you're only making a few short journeys or a pre-planned fixed-itinerary trip around Europe, you're almost certainly better off buying ordinary point-to-point train tickets (as far in advance as possible).
2. For long-distance, spontaneous and/or flexible trips a Eurail pass is best (especially for Eastern Europe). But don't forget when travelling in Western Europe (France, Germany, Switzerland, Italy, Spain) to book seat and sleeper reservations which are an extra cost (as far in advance as possible to get the cheapest fare). A rail pass gives you the flexibility to change your mind and your plans as you go, you can just throw away any reservation and buy another reservation locally based on your new plans. Read more on choosing a Eurail pass.
3. In peak season (June, July and August) trains on popular routes are often fully booked so securing your seat / sleeper reservation early is a must! May and September can also be busy.
4. Italy deserves a special mention, as it's such a popular destination. Rail passes for Italy only make sense if you plan to do the equivalent of Rome-Venice every time you step onto a train. They do not make financial sense if you're only going Rome-Florence day 1, Florence-Venice day 2, Venice-Verona day 3, etc.

Don't be afraid to mix & match a railpass with one or more point to point tickets. For example, for 11 days of train travel in Europe, it's cheaper to buy a 10-day Eurail Global pass plus one point-to-point ticket for the shortest/cheapest of all your train rides, than to buy the next pass size up, which is the 15-day Eurail Global pass. If the start of your trip is known and fixed, the rest flexible, you could buy a cheap ticket for the first one or two journeys, then start using a railpass.