Something I've only started doing recently (thanks to prodding by Sir Will and Asiatic Fox) is infusing white, green and Oolong tea. I knew you could, and had tried my hand at it a number of times. But every attempt was a small failure and I'd resigned myself to black tea and one time around with non-black teas.
Not anymore. I'm steeping green tea, drinking that pot, infusing it again, drinking the second pot and in some cases I'm able to even get a decent third infusion out of the same sock/bag of tea. A few things I've read or figured out: don't use boiling water if you're going to attempt this. You shouldn't be using boiling water with non-black teas anyway, but especially if you want to infuse the tea.
Every tea has an optimal water temperature. I get a ballpark figure from different tea sites (like steepster.com or ratetea.net), but ultimately you have to figure out the perfect temperature yourself. 80 degrees centigrade seems to be good for most green teas. That's my best estimate so far.
Let me know if you've tried this and what your experience has been.
Drink better tea.