AES - MixColumn transformation using the identity matrix
If you eliminate the MixColumn (or equivalently, replace it with an identity Matrix), then the resulting cipher will effectively be 4 independent 32 bit block ciphers.  This happens because what happens in one 32 bit row no longer has any propagation to any of the other 3 32 bit rows.

This results in a much weaker cipher; not only would that bring up possible chosen plaintext/ciphertext attacks (where you modify one of the 32 bit blocks, but leave the other 3 the same), you would also have ciphertext only attacks with a birthday bound of circa 256k...