This obviously includes the 10 commandments and the instructions He gave to Israel, but also includes the things he lead his Holy Spirit to direct the prophets and apostles to say and what he directed Jesus to say and do (since Jesus only ever spoke as God the Father directed Him).
I would think there are a few, given the nature of His position of authority over all creation. However, the question would be answered differently if you are referring to God as the Godhead (ie, the Trinity) or just as God the Father.
If you are just referring to God the Father, then the answer is any form of submission. God commands us to submit to the government, but He Himself does not submit to any government of man. (As we know from the New Testament, Jesus did submit to the government, and a sinful one, lest we forget).
The Bible tells us Jesus fulfilled the law, and never sinned (1 Peter 2:22) so therefore Jesus completely fulfilled all requirements that men had from God, so in that sense, no, God did not command anything that He (Jesus) did not Himself fulfill.