This is an odd issue that there have been quite a bit of discussion about even on this forum. Possible suggested issues range from insufficient power to bad internal hardware design of the pi.
When Edimax EW-7811UN usb adapter is plugged in pi reboots instantly.
I have ruled out the power supply by using 2 different ones for testing (1.5A wall plug and 2A open frame psu). I tried 3 different raspberry pi's bought at different times all with same issue. I also tried different sd cards, and even operating systems (Raspbian, RaspBMC). I ran rpi-update on a clean Raspbian OS install (NOOBS 1.3.7, NOOBS LITE 1.3.5).
I measured the voltage at test points and got around 4.5V when booted.
The only thing that seems to work is strangely plugging the usb adapter via an old usb extension cable I had lying around (it could even be rated for usb 1.1 use if that matters).
Why would a simple usb extension solve the problem? It almost seems like pi resets purposely as soon as it detects a device is connected.