Issue while connecting ESP8266 with Arduino Mega. It always says “Module have no response.”
Your transmitter and receiver pins need to be crossed, rx->tx and tx->rx. As a mnemonic, the two ends of the antenna point to the board edge with the receiver pin and it is that pin that needs the voltage divider. While you're at it, it would be a good idea to tie the RST pin high, as well as the CH_PD. I use one 10K pullup for both.

Recent versions of these boards are shipped with their baud rates set to 115200. Since you're using a hardware UART on the Mega board, you can send/receive to it at that rate. 

Note to readers using a software UART (SoftwareSerial): First thing, change the board's baud rate to 9600 and communicate with it at that rate. You can use SoftwareSerial to make the change as it sends at 115200 reasonably reliably, but its receive function can't keep up at that rate).

You can confirm your connections and baud rate with:
EspSerial.println("AT");
You should receive `OK' in reply.