Is it possible to find the key for AES ECB if I have a list of plaintext and corresponding ciphertext? Assume I have a list of plaintext text and its corresponding ciphertext which was created using a specific key with AES in ECB mode. 

Can I recover that key?

If, how big does the list of plaintext and matching ciphertext have to be to be able to find it in a feasable amount of time (say in 1 or 2 hours)?
Assume I have a list of plaintext text and its corresponding ciphertext which was created using a specific key with AES in ECB mode.
Can I recover that key?

No.  This is what is referred to as a known plaintext attack, and secure block ciphers are designed to prevent exactly this kind of attack.  This answer on the Mathematics Stack Exchange goes into more detail about the notion of IND-CPA (&quot;indistinguishability&quot;) which AES is conjectured to meet and how that implies that a known plaintext attack is impossible.