In all honesty I didn't knowledgeably choose train travel as my preferred method of transportation around Europe. Instead it came about as a direct result of my sheer ignorance of budget airline carriers and the shiny advertisements for Eurail passes (they promised maps and fancy looking tickets okay!). Despite not having researched it fully the first time around, let me tell you now that it is certainly not a bad thing. I have since discovered that although train travel can be a bit arduous and not overly comfortable, it is decidedly more pleasant to spend 5 hours on a high speed train than 2 hours traveling super economy in a flying tin can.
Traveling by rail allows you time to read, write, play a few games of solitaire or poker and best of all it allows you the freedom to get up and stretch your legs whenever you want! Air pressure ear pops are limited to trains that pass through tunnels or climb up mountains, the seats are bigger and usually less cramped plus you get to see some absolutely amazing scenery along the way.
If you get the right combination of deals (Eurail, railpass etc) you can also very easily make train travel the most cost effective solution for your grand tour. Investigate how many times you will be traveling within one country, how often will you be using international rail services, how close are the stations to your hotel, how frequent are the trains? You can use these questions to ascertain whether or not a rail pass is best for you or if its better for you to buy your own point to point tickets.
I talk about this now because it was at this point of my journey that our painfully disrupted train trip from Nice to Milan, involving faulty train carriages, canceled seat reservations and angry Italian mothers, led to a chance meeting with two lovely ladies, a deck of cards and a train trip of raucous card games and laughter. It reminded me of how much fun I have had on my train trips. What it boils down to is simple, you have nowhere else to be and you can't help what time you arrive, so you can just sit back and enjoy the journey (Remind me to tell you about some of my ...Err... less relaxing train journey's sometime).
Two final points...
Buying your tickets in advance through the local rail company (Trenitalia in Italy, TGV in France, Renfe in Spain or Deutsche Bahn in Germany etc) is usually cheaper than leaving it until the last minute or going through a third party provider. So if you have the nouse I suggest you attempt it yourself.
Be aware of your alternatives and try not to hinge your entire journey on one train leg being on time. You are well aware of how the trains in your home town are frequently delayed, so be aware that it is the same in the new city you are visiting and it is no one else's fault but your own that you only left yourself 10 minutes to change trains.
Train travel around Europe is by far the most comfortable and satisfying way to get from amazing A to beautiful B! (Yep I came up with that one all by myself) and who knows, you might end up sitting opposite a new friend*.
*Disclaimer: New friends are not guaranteed. I take no responsibility if you are seated next to a... less than desirable... train buddy. If you are seated next to an undesirable, I suggest you swiftly occupy whichever senses are being assaulted (I have been known to shove my nose in a bottle of orange juice to achieve this).