One of the things that took me a long time to figure out is that often, flying through 2-3 different cities on a single ticket often costs very similar to a one-way flight.
So, going "New York to Berlin on May 25th" might not be cheaper than going "New York to London on April 28th, London to Munich on May 22nd, Munich to Berlin on May 25th" -- strange but true.
It's especially easy to stop in hub cities for up to a month, so swinging through Chicago, New York, Los Angeles, London, Tokyo, Hong Kong, and other regional hubs is easy. It's fun to stop in New York for 2-3 days when you're on your way elsewhere if you've got the time.
The thing is, it can be tricky to plan these routings. That's where Matrix comes in --
People don't link to it much, since you can't book directly from it. But it's incredibly useful at figuring out interesting flight routes -- they've got most of the spectrum of possible flights covered except possibly some discount carriers.
Matrix is robust: it's the back-end for most of the flight search engines like Orbitz and Kayak. Again, you can't book directly from it, but it lets you piece together which cities and dates coordinate well together.
My favorite feature on it? You can click the "Nearby" link next to any airport you enter, and search airports within a large possible range of nearby airports. If you want to really go crazy, you can search something like "within 500 miles of this airport" -- so if you just want to land on Continental Europe, in Japan, or anywhere in China, you sometimes find cheap, fun, or available fares to airports you never would have guessed to go on your own. Then you can grab rail or a discount flight to get to whatever city you wanted to start from.
It's probably not the best tool for new travelers -- I'd recommend you start with kayak.com or kayak.com/explore (which has a wonderful "where can I go for how much?" feature from any airport, which is easy to use and great).
But once you're starting to get into more advanced travel, definitely check out Matrix. You can do some really cool things with it once you get the hang of it.