Thanks! I've been slowly teaching myself electronics for the past few years (as a hobby). I recently got an oscilloscope and it opened a whole new world for me!
I cut one of the ear buds from an old pair of headphones. Connected it to the scope and got a cool visualization of the music being played.
Beyond that, the biggest benefit of the Oscilloscope was it let me learn about and build oscillators and op-amps. For instance, I made a relaxation oscillator a few days ago (produces low frequency square waves).
I recently also got two electronics learning lab. I got the 300-in-1 from Elenco. Radioshack also has a similar one. The material that comes with the lab is strange - on the one hand, the projects are pretty sophisticated. On the other, there is little to no explanation on how they work. But I've found that this is great for self-study. The oscilloscope has been very handy for this part.
P.S.1 Someone showed me a cool trick with an oscilloscope at maker faire. You need two signals out of phase. Go into X-Y mode and voila ... you get some cool annimated drawings :)
P.S.2 Be careful and safe playing with electricity!
I'd also suggest the following playlist on YouTube. The army/navy/air force videos are amazing! http://www.youtube.com/playlist?list=PLAA9B0175C3E15B47