Which ciphers produce random ciphertext? I already know AES produces a "random" output.
5e4e6440826d6afc4535fbf078455f791159701a9df624ddd4e4dda84523b6a7
Its ciphertext doesn't follow a pattern and is indistinguishable from noise.    

Is this common for most ciphers?
Strictly speaking, we can't know for sure that the output of AES is indistinguishable from random noise. It's conjectured to be true but no "proof" of that fact exists. 

For most commonly-used ciphers, it is conjectured that their output is indistinguishable from random. Specifically, modern ciphers are conjectured to be "strong pseudorandom permutations", which means that an adversary given encryption and decryption oracles for the cipher can't distinguish it from a random permutation.