Should we love Satan since he is our greatest enemy? Jesus asked us to love our enemy Mat 5:43-44:


  43“You have heard that it was said, ‘Love your neighbor and hate your enemy.’ 44But I tell you, love your enemies and pray for those who persecute you,


So, should we love Satan?
Our command to love our enemies is intended for our human enemies, whom God also loves.  God's love for us is shown through His sacrifice on the cross, and also in the statement that it is His desire that every man come to repentance.

Satan, on the other hand, cannot come to repentance, and there is no hope for his redemption.  

A good answer with scripture references can be found here: Should We Love Satan?

The following is copied directly from the article:


  A young girl asked me this question: "Should we love Satan?" She
  clarified her question by saying Jesus taught us to love our enemies
  (Matthew 5:44-45) and that Satan is our enemy (1 Peter 5:8).
  
  After careful consideration of the question, I answered something like
  this. All of mankind has hope; the apostle Paul said he had a goal or
  an aim to "... present every man perfect in Christ Jesus" (Colossians
  1:28). We are to seek every man's highest good -- that is to love him
  that he might be saved. On the other hand, Satan's eternity has been
  sealed, there is not anything that man can do or should do to change
  that. We are told that Satan has gone forth with great wrath because
  he knows that he has but a short time (Revelation 12:12). Jesus tells
  us that he has prepared a lake of fire for the devil and his angels
  (Matthew 25:41).
  
  What should be our attitude towards Satan? We should follow the
  example of Michael the archangel who refused to get involved with
  Satan, even in a discussion. Michael was willing to leave Satan in
  God's hands. He said, "The Lord rebuke thee" (Jude 9). Our attitude
  towards Satan should be to resist him. God said, "Resist the devil,
  and he will flee from you" (James 4:7). We are to be on guard and
  watchful because Satan is our enemy trying to devour us (1 Peter 5:8).
  
  Satan has many devices; he is tricky. He is trying to lead us to the
  grave separated from God (2 Corinthians 2:11). He is trying to blind
  our minds to the word of God through unbelief (2 Corinthians 4:4).
  
  We are not instructed in the inspired scripture to love Satan, but to
  overcome him. The only way we can do this is to fill our hearts with
  the word of God (1 John 2:14). Jesus is our example; Satan threw
  everything he had at Jesus -- the lust of the flesh, the lust of the
  eyes, and the pride of life -- and each time Jesus would answer, "It
  is written." He defeated Satan with the word of God, and He did not
  try to convert him (Matthew 4:1-11) because Satan's eternity in the
  lake of fire had already been sealed.
  
  In the context of Matthew 5, when Jesus said, "Love your enemies," He
  was discussing our relationship with our fellow man and not with
  Satan. 
  
  Roy Dunavin West-Ark Church of Christ, Fort Smith, AR


In addition to the above, your question ignores the context.  

The verse is in the midst of a series of "You have heard it said" statements that show that the Old Testament law is the bare minimum of what is required for righteousness, and in this example, the statement that we should love our enemy was "You have heard that it was said, 'Love your neighbor'"  The essence of the verse is (like the surrounding verses) that the law says to do this, but the true requirement for perfect love and righteousness is to do this more perfect fulfillment of the law of love...

In the context of this verse, "thy neighbor" was clearly meant to denote human relationships.  There is no reason, other than to set up a straw-man argument, to believe that "your enemy" is meant to be viewed in a different context.