Is there a website to search for European train tickets? I mean something like kayak.com, expedia.com, airfare.com, etc for trains? I know there are specific countries' website like bahn.de, sbb.ch, voyages-sncf.com, etc. But is there a website to search and see the prices easily without having to go through many steps?
There are some offers that start appearing on the web:
http://mytripset.voyages-sncf.com offers flights and trains (apparently it's possible to book some outside France [it's a French travel agency] but I cannot guarantee it).
In any way, as Mouviciel suggested, you can query trains in Europe from the German/Swiss/Austrian providers but not book tickets out of these countries. You can have a lot of information on the trains (like all stops) and I use it sometimes for any train in Europe. It includes some local transit system.
More generally, there is an answer that will probably help you.
Unfortunately, pricing and booking is not available on these sites beyond domestic routes and some international ones.
The best site that gather information about train travel in Europe is Seat 61.
This forum post just popped up in my alerts because it mentions Loco2. I'm co-founder of loco2.com so don't want to get lambasted for self-promotion, but actually @Vince isn't quite right. Loco2 has print at home tickets for lots of trains (Eurostar, TGV, ICE trains etc) which means it doesn't matter where you are.
We're integrated with the French and German (SNCF & Deutsche Bahn) rail booking systems and usually have print at home or collect at station tickets for domestic tickets in those countries, as well as international trains that cross their borders. We have some tickets from other operators via indirect connections, and it is these that are only able to be delivered to the UK.
@mouviciel is right though that sites using Hafas have the most comprehensive timetable information, but see Jamie's comment about the difference between Hafas (the journey-planning engine) and Merits (the timetable data) (Loco2 does not currently use Hafas/Merits).
One service that hasn't been mentioned yet is Waymate. They are somewhat like Hipmunk but for train travel. Waymate has the potential to become awesome once they add flight search. Good combined flight and train search is something that would be very useful in Europe.
Personally, I use bahn.hafas.de for finding train connections. In fact, when I once asked someone in Russia to help me find a train connection, I was quite surprised that he used the same service and not that of Russian Railways. Hafas has a really good database, nowadays even with real-time updates to the schedule, and when searching I can specify that I have a BahnCard, which gives me price reductions.
Generally, trains in Europe are either local or long-distance. The local ones sell tickets on the same day at the station and are fairly cheap. The long-distance ones offer much more comfort, for a higher price, and only between cities. I feel like 3-4 hours on a normal train is my limit and anything more than that and you'll want something better.
Some trains (ie. Amsterdam -> Brussels) run every day at the same time and you don't get a seat number - so you can get your ticket ahead of time and just show up and go on the day you want.
However, the Thalys and ICE are the nicest and best trains but also priciest. The comfort is similar or better than that of an airplane. Book early enough and you might get a nice discount. They often run specials available on their website (http://www.thalys.com/ and http://www.bahn.com/i/view/USA/en/trains/overview/ice.shtml)
For checking schedules you can rely on the site of the German railways, already mentioned in this thread. That should be sufficient for most of your needs.
Unfortunately, when it comes to booking, the situation is not as good. There is no single website for booking trains in Europe, like you can find for e.g. flights. The best strategy is to use the sites of the national companies of the country of departure or the country of arrival. You can google for these sites or you can use the excellent seat61.com to find the addresses. Sites à la loco2.com provide a more user-friendly interface than some railway companies. But, you cannot use them to book anything you want to. They are limited in their possibilities, just as the national sites.
Example. Let's suppose I want to travel from Brussels to Gdansk somewhere in March. Loco2 doesn't show anything. However, the German Bahn gives me a list of connections. None of these can be booked directly. For the booking I have to split my trip into 2 parts. First I will have to buy a ticket from Brussels to Cologne, via bahn.de or thalys.com. Next I will have to book a ticket from Cologne to Gdansk, via bahn.de. This may look a bit cumbersome, but it is funny. Your trip starts at home :-)
If you find this horrible, note that until not so long ago, it wasn't even possible to buy international tickets online. Things are changing into the good direction. And seat61.com really helps a lot to find the good way through the jungle!
www.bahn.de will show you prices, and sell you tickets for trips from Germany to most neighbouring destinations. Another good site is www.b-europe.com. This is the international booking site of the Belgian railways, an there is www.ns-hispeed.nl which is basically the same booking engine, but for the Dutch railways. www.sbb.ch is good for trips from Switzerland.
loco2.com, mentioned above however has failed to provide me with solutions for all of the origin - destination pairs I entered. Maybe because they're linked to the French system, which doesn't like to give solutions involving many transfers.