The amazing thing I have discovered recently as a major benefit of having learned Swedish is that I can also understand Norwegian and Danish (at least in writing).
I could hardly believe Swedes at first when they told me they pretty much understand Norwegians since their languages are so similar. Few Swedes that I've met can understand spoken Danish (they joke about it sounding like they have oatmeal in their mouths), but they've claimed they can at least read it.
I've been on several Danish sites, and to my delight, have discovered that I can pretty much understand what they are saying. And just the other day, I decided to Youtube a Norwegian TV show just to see if I could understand it, and to my delight, I could (most of it, anyway!). I now understand the claims of Swedes mentioned above. Then it gets me thinking - if I can understand as much as I do, imagine just how much, for instance, my J understands. It's really a pretty cool phenomenon.
As a native English speaker, I've really never felt like I've "basically understood" any other language than my own. When learning Spanish and realizing that a lot of words are similar to English it was like a revelation. But I could never just read Spanish without having formally learned it in class and say "Oh, I understand!" the way I've been able to when coming in contact with Norwegian and Danish. It makes me feel pretty awesome to have gained a basic understanding of two other languages in the process of learning Swedish. 8)