Only with ESP8266: "avrdude: stk500_recv(): programmer is not responding"

I have 2 Arduino UNO's and three ESP8266 (two shields and one simple fella). The Arduno's work fine with everything else, but when I connect any of my ESP8266 to either of my Arduino's, i get the dreaded message:

avrdude: stk500_recv(): programmer is not responding
avrdude: stk500_getsync() attempt 1 of 10: not in sync: resp=0x00
... and so on

I would like to get my WiFi on, but my Ardunio's don't want to cooperate. Any ideas?

Ubuntu 15.10, 64-Bit.
IDE: 1.6.7

It would help if you could provide more information on how you are connecting the ESP to the Arduino.

One of them is a shield from SparkFun (https://www.sparkfun.com/products/13287). It is just connected like a normal shield. Actually I have two of these, and both have them give the same error.

The other one is a small cheap one like this:

It is connected like this:

The wierd thing is that the small cheap one gives the exact same error.

AND this is happening one two different Arduino UNO's...

When you program the UNO using USB it communicates with the '328 via pins D0 & D1. The ESP8266 is interfering with this process.

Try using SoftwareSerial to communicate with the ESP8266 on different pins?

I am not quite sure what that means. How would I go about doing that?

#include <SoftwareSerial.h>
SoftwareSerial MySerial(7, 8); //Pick a more meaningful name!

Connect the ESP8266 Tx to D7, Rx to D8

Then instead of Serial.whatever use MySerial.whatever.

That is fantastic! That worked like a charm!

I only had to change it to

#include <SoftwareSerial.h>
SoftwareSerial MySerial(8, 9);

for my shield, because it had SW_TX on 8 and SW_RX on 9.

Thank you SO much!