Connecting Arduino Uno to ESP8266
The Arduino Uno has a 3.3V linear regulator (LP2985) onboard. The 3.3V is available on the power connector. The problem is that such regulator only provides 150mA, which is not enough for the ESP8266 at full power.

A capacitor might be necessary, but it would solve the problem only if the ESP8266 has just few burst of high current usage, while spending most of its time at low current consumption.