These steeping times are only approximate, and you should adjust them depending on your own personal tea taste.
Black tea - Black is the most robust of the tea varieties and can be brewed in truly boiling water, usually steeped for 4-6 minutes.
Oolong tea - As to be expected, oolong tea falls between green and black. The best temperature is around 190F. But oolong should be steeped longer than black tea, for around 5-8 minutes.
Green tea - You will need to be more gentle with your green teas. The water temperature should be around 150-160F and only steeped for 2-4 minutes.
White tea - Another delicate tea that should be treated gently. Water can be a bit warmer than for green tea, at 180F. You should let it steep longer though. At least 4-6 minutes.
Rooibos tea - This red herbal tea from South Africa is very hardy stuff and should be prepared with fully boiling water, just like black tea.
Most herbal teas - With so many different herbs that can be used for herbal tea blends, there is no way to give any temperature or steeping guidelines with any accuracy. Most herbs can be brewed in boiling water and steeped for about 5 minutes. You might need a bit of trial and error to get the perfect cup.
If you don't have a thermometer handy, you can tell the water temperature by watching the bubbles. Small bubbles will float to the surface of the water 160-170F, and you'll see strings of bubbles from the bottom of the kettle at 180-190F. After that, you'll have a full rolling boil.