Meet the smallest Arduino board (or not?) on the world called PICO. What is the best feature of board? The dimension - 0.6" x 0.6" (15.2 x 15.2 mm).
The board contains ATmega32U4. It supports native USB. The headers are 0.1" (2.54mm) and you can use the PICO on breadboard.
The board includes micro USB connector, LED and button and it is supports in Arduino IDE.
The price starts from $18.
Other really small Arduino board is Beetle by DFrobot.com
https://www.dfrobot.com/product-1075.html. The Beetle is usually to buy for $7.9 + shipping.
The dimension of board is 20x22mm, it also contains ATmega32u4 microcontroller.