That is the wonderful thing about European trains - if you do miss one, unless it is late at night, it isn't that long until another one comes along. Here where I live - if you miss the Via Rail, it only runs 3 (or 4) days a week now from Nova Scotia to central Canada - so if you miss it, you are sh!t out of luck!
Having been back over a few times (and always back to Italy)...we learned not to 'cheap out' on the trains. Now, I always look at time vs money (and for me, time is money). If the fast train doesn't cost much more (say, 10-15 euro vs slow train) but arrives 60min + earlier, I'd pay the extra to give me more time in the place I'm going instead of wasting it sitting on a train...works for longer distances obviously, as opposed to short trips.
When we did the Rome-Pisa portion of our trip, we planned on having 3 hours or so to wander to the Tower before having to catch the train to Cinque Terre. Because of the late arrivals, we ended up only having 2 hrs (the more I think of it, the more I'm sure the train was 40-60 min late after all the delays and stops). We had to rush thru a little more - because we had to get to Corniglia (CT) by 7pm as we thought that was the last time the shuttle bus ran to the village center and we didn't want to schlepp up the hundreds of steps to the top with our bags. Throw in there our screw up getting off in Carrera and we had some panicky moments. But we made the shuttle.
For my upcoming trip in Sept, I finally prebooked the fast train from Rome to Venice to get a good discount. I don't necessarily liked to be tied into a rigid schedule in case I want to linger (in 2010, I thought of booking Venice-Florence in advance and was glad I didn't as we ended up lingering in Venice for another 2-3 hrs after we thought we'd go - I love Venice, it was a gorgeous sunny day - what can I say?!).