I was thinking about purchasing the tickets at the local stations. I wanted to spend three weeks in Poland and a week in Prague, Munich, and Hamburg. I set aside $300 for each train itinerary but I'm not sure if that's enough.
You may be able to make a Eurail Pass work for you.
Eureka! - There are "Select Passes" allowing 3 or 4 or 5 countries of your pecification. These were not shown in the general menu.
Eurail 2013 routes map PDF download. Large and impressive.
These are usually 2 country passes allowing N days of travel within an overall period. Adding the extra country may make individual pricing cheaper.
I did some checks on prices for you. Prices are from Bahn.de. Please verify this yourself as well.
A 5 day Eurail Select pass would be $320. So based on these prices, it's a pretty close call.
300 USD should even be enough to cover all these itineraries. To know the exact price for tains to and from destinations in Germany, you can have a look at http://www.bahn.de
For the tickets from Krakow to Prague you can have a look at http://www.polrail.com . Or try at the station in Krakow. The Czech railways only allow booking into the other direction.
The price eventually depends on how early you book, how much comfort you choose and how flexible/restrictive tickets you buy.
I know that there are Interrail or Eurail passes. They might be worth a look only if you are less than 26 years old. But even in that case, you will probably be better off by buying point to point tickets.
As an example, here are some quotes for 2nd class travel, with a departure in three weeks, on a weekday.
Krakow – Prague : 76 USD (www.polrail.com)
Prague – Munich : 25 USD (www.cd.cz)
Munich – Hamburg : 88 USD (www.bahn.de)
Hamburg – Warsaw : 55 USD (www.bahn.de)
= 244 USD
Have you considered a Eurail pass? This allows travel on European railways for a fixed set price. Current prices start at USD $313 (for your entire trip) for those three countries if you are 25 or younger.
A pass like the Eurail Pass (and the Interrail Pass) was once a great way to travel around Europe. You could just hop on and off trains at leasure. However, these days are mostly gone. Many long distance trains require reservations, which mean you need to go to the station to get them anyway, and often there are limited contingents for pass holders. In practice it is now best to just buy long segments online in advance to take advantage of advance purchase deals, and for short trips just to buy them locally at the station on the day of travel.