Is there a commandment to love your parents? In Exodus 20:12 or Deuteronomy 5:16 (i.e. in the ten commandments), it states that you should honour your father and mother. I have often heard that we are commanded to love our parents: is this just folk-religion? Is there a Biblical commandment to love your parents? Is this just loving your parents as part of loving your neighbour (e.g. Mark 12:31)? Or is there a specific commandment?
No, there is no specific commandment to, 'love,' your parents.

Neither the Hebrew, 'ahav,' or the Greek, 'agape,' which may fairly be described as, 'love,' are commanded with regard to parents.  We are however commanded to both, 'ahav,' and, 'agape,' almost everyone else, from The Lord to our enemies.

I guess it is assumed that we will love our parents regardless, and only have to be commanded to honour / fear / obey them.

Ahav:
http://www.blueletterbible.org/lang/lexicon/lexicon.cfm?Strongs=H157&amp;t=KJV

Agape:
http://www.blueletterbible.org/lang/lexicon/lexicon.cfm?Strongs=G25&amp;t=KJV

As to, 'honouring,' parents in the Ten Commandments, the root word is, 'kavod,'  which implies weight, glory, or wealth.  We are commanded to obey our parents as people who deserve great respect, but not to love them in the emotional sense.

Ex 20:12 Ex 21:15 Ex 21:17 Lev 19:3 Lev 20:9 Deu 5:16 Deu 21:18-21 Mat 19:17-19 Mar 7:9-13 Eph 6:1-2 (incomplete list, various root words)

However, honouring parents is secondary to obeying the Lord.

Deu 33:8-11 Mar 10:28-31 Luk 12:51-53 (incomplete list)