Book travel within Europe in advance?

It is a question of your comfort level and flexibility. We often book first and last night just so we know where we are at that time. In between it is a mix. Rarely book transportation ahead of time but realize that we can miss some discounts if using the faster trains. No discounts on slow trains. The local TI can always give recommendations for local housing but it does take time to pin that down. Some times just calling ahead a couple of days is adequate. A side comment on questions you didn't ask - No way you can hit those cities in 16 days without spending 8 days inside a train car. Also consider open jaw ticket like into Dublin and home from Rome if you insist on those cities.

Since you have long distances in a relatively short time, I assume you will be flying for some of that? If so, the budget airlines should be booked well ahead to get the deals. Something like a train between Venice and Rome, I would wait until I get there. If you are doing an overnight train, book those ahead as well. As for lodging, much debate there. If you will be locked into dates due to flights, then you might as well locate a hotel and try to book. Depending on time of year, the cities you are going to tend to be busy and rooms fill up. If you had smaller towns or off-season, then you could leave a few nights open and find something when you get there.

Our plan is to arrive in Dublin on Wednesday morning, quick flight to London Friday, train to Paris Monday, flight to Rome Thursday, train to Florence for a night on Monday to see a friend, train to Venice Tuesday morning, flight to Madrid Wednesday, home to Boston Saturday. We're not looking for an in-depth trip to any of these cities, just a quick visit to check things out. I suppose the real question is, is it more cost-effective to book now or wait til we get there?

ps, our travel dates are March 28- April 14, which is not flexible due to our work schedules. Our itinerary between Dublin and Madrid is still flexible at this point. Also, if it is a better idea to book in advance, how far in advance should we do so?

The Eurostar from London to Paris is generally cheaper the farther ahead you book it. I would definitely book that one now. The ES trains in Italy from Rome to Florence and Florence to Venice also offer discounts for advance purchase, so I would book those as well on Trenitalia.com. I cannot speak to the flights as we've used those.

Yes, definitely book your flights ahead, the earlier the better! You don't say when you are traveling (unless I missed it in a subsequent post), so I can't speak to when to do it, exactly. Watch the fares of the various airlines for awhile to see how their fares usually run, then book when you see a deal. I always figure that anything I can book ahead saves me time once I'm there. You don't really want to be trying to book flights once you are in Europe. Edit: I now see the travel dates. With so much time, my original advice stands. Watch the fares and check out all of the options. Then you will know when a deal is good (like Ryanair's or EasyJet's occasional 1 euro fares).